diff --git a/GSASII/GSASIIphsGUI.py b/GSASII/GSASIIphsGUI.py
index e2243114..307fba61 100644
--- a/GSASII/GSASIIphsGUI.py
+++ b/GSASII/GSASIIphsGUI.py
@@ -1645,7 +1645,7 @@ def OnPhaseName(event):
'called when the phase name is changed in "General"'
event.Skip()
newName = NameTxt.GetValue().strip()
- renamePhaseName(Item,generalData,newName)
+ renamePhaseName(G2frame,data,Item,generalData,newName)
NameTxt.SetValue(newName)
def OnPhaseType(event):
@@ -5774,7 +5774,7 @@ def OnReplacePhase(event):
newname = rd.Phase['General']['Name']
data['General']['Name'] = phsnam
# rename phase to new name from file
- renamePhaseName(G2frame.PickId, data['General'],newname)
+ renamePhaseName(G2frame,data,G2frame.PickId, data['General'],newname)
# force a reload of current tree item
G2frame.PickIdText = []
wx.CallAfter(G2gd.SelectDataTreeItem,G2frame,G2frame.PickId)
@@ -13264,39 +13264,6 @@ def rbKeyPress(event):
G2frame.Raise()
return
- def renamePhaseName(phaseItem,generalData,newName):
- '''Called to rename the phase. Updates the tree and items that
- reference the file name.
- '''
- oldName = generalData['Name']
- phaseRIdList,usedHistograms = G2frame.GetPhaseInfofromTree()
- phaseNameList = usedHistograms.keys() # phase names in use
- if newName and newName != oldName:
- newName = G2obj.MakeUniqueLabel(newName,list(phaseNameList))
- generalData['Name'] = newName
- G2frame.G2plotNB.Rename(oldName,generalData['Name'])
- G2frame.GPXtree.SetItemText(phaseItem,generalData['Name'])
- # change phase name key in Reflection Lists for each histogram
- for hist in data['Histograms']:
- ht = G2gd.GetGPXtreeItemId(G2frame,G2frame.root,hist)
- rt = G2gd.GetGPXtreeItemId(G2frame,ht,'Reflection Lists')
- if not rt: continue
- RfList = G2frame.GPXtree.GetItemPyData(rt)
- if oldName not in RfList:
- print('Warning: '+oldName+' not in Reflection List for '+
- hist)
- continue
- RfList[newName] = RfList[oldName]
- del RfList[oldName]
- # rename Restraints
- resId = G2gd.GetGPXtreeItemId(G2frame,G2frame.root,'Restraints')
- Restraints = G2frame.GPXtree.GetItemPyData(resId)
- i = G2gd.GetGPXtreeItemId(G2frame,resId,oldName)
- if i: G2frame.GPXtree.SetItemText(i,newName)
- if len(Restraints) and oldName in Restraints:
- Restraints[newName] = Restraints[oldName]
- del Restraints[oldName]
-
#### UpdatePhaseData execution starts here
# make sure that the phase menu bars get created before selecting
# any (this will only be true on the first call to UpdatePhaseData)
@@ -13652,3 +13619,36 @@ def saveIsoNewPhase(G2frame,phData,newPhase,orgFilName):
G2frame.GSASprojectfile = f'{s[0]}_{num}.gpx'
G2IO.ProjFileSave(G2frame)
return G2frame.GSASprojectfile
+
+def renamePhaseName(G2frame,data,phaseItem,generalData,newName):
+ '''Called to rename the phase. Updates the tree and items that
+ reference the file name.
+ '''
+ oldName = generalData['Name']
+ phaseRIdList,usedHistograms = G2frame.GetPhaseInfofromTree()
+ phaseNameList = usedHistograms.keys() # phase names in use
+ if newName and newName != oldName:
+ newName = G2obj.MakeUniqueLabel(newName,list(phaseNameList))
+ generalData['Name'] = newName
+ G2frame.G2plotNB.Rename(oldName,generalData['Name'])
+ G2frame.GPXtree.SetItemText(phaseItem,generalData['Name'])
+ # change phase name key in Reflection Lists for each histogram
+ for hist in data['Histograms']:
+ ht = G2gd.GetGPXtreeItemId(G2frame,G2frame.root,hist)
+ rt = G2gd.GetGPXtreeItemId(G2frame,ht,'Reflection Lists')
+ if not rt: continue
+ RfList = G2frame.GPXtree.GetItemPyData(rt)
+ if oldName not in RfList:
+ print('Warning: '+oldName+' not in Reflection List for '+
+ hist)
+ continue
+ RfList[newName] = RfList[oldName]
+ del RfList[oldName]
+ # rename Restraints
+ resId = G2gd.GetGPXtreeItemId(G2frame,G2frame.root,'Restraints')
+ Restraints = G2frame.GPXtree.GetItemPyData(resId)
+ i = G2gd.GetGPXtreeItemId(G2frame,resId,oldName)
+ if i: G2frame.GPXtree.SetItemText(i,newName)
+ if len(Restraints) and oldName in Restraints:
+ Restraints[newName] = Restraints[oldName]
+ del Restraints[oldName]
diff --git a/GSASII/GSASIIpwdGUI.py b/GSASII/GSASIIpwdGUI.py
index 88c456e6..3e141cd4 100644
--- a/GSASII/GSASIIpwdGUI.py
+++ b/GSASII/GSASIIpwdGUI.py
@@ -20,6 +20,7 @@
import random as ran
import pickle
import scipy.interpolate as si
+from fractions import Fraction
from . import GSASIIpath
from . import GSASIImath as G2mth
from . import GSASIIpwd as G2pwd
@@ -38,7 +39,15 @@
from . import GSASIIsasd as G2sasd
from . import G2shapes
from . import SUBGROUPS as kSUB
-from . import k_vector_search as kvs
+from GSASII.imports.G2phase_CIF import CIFPhaseReader as CIFpr
+from . import GSASIIscriptable as G2sc
+from . import GSASIImiscGUI as G2IO
+try:
+ from sympy import symbols, nsimplify, Rational as SRational
+except ImportError:
+ G2fil.NeededPackage({'ISODISTORT k-vector search':['sympy']})
+ symbols = None
+
try:
VERY_LIGHT_GREY = wx.SystemSettings.GetColour(wx.SYS_COLOUR_BTNFACE)
WACV = wx.ALIGN_CENTER_VERTICAL
@@ -4503,7 +4512,7 @@ def LoadUnitCell(event):
# TODO: I think this used to work, but this needs to be revisited due to
# AttributeError: 'G2DataWindow' object has no attribute 'ReImportMenuId'
- # from:
+ # from:
# reqrdr = G2frame.dataWindow.ReImportMenuId.get(event.GetId())
#
# def ImportUnitCell(event):
@@ -4601,6 +4610,7 @@ def SeaResSelected(event=None):
Generates & plots reflections
'''
+ from . import k_vector_search as kvs
data = G2frame.GPXtree.GetItemPyData(UnitCellsId)
cells,dminx = data[2:4]
if event is None:
@@ -5164,8 +5174,9 @@ def strTest(text):
G2frame.OnFileSave(event)
wx.CallAfter(UpdateUnitCellsGrid,G2frame,data)
- def OnISODISTORT_kvec(phase_nam): # needs attention from Yuanpeng
- '''Search for k-vector using the ISODISTORT web service
+ def OnISODISTORT_kvec(event):
+ '''Search for k-vector using the ISODISTORT web service.
+ Developed by Yuanpeng Zhang with help from Branton Campbell.
'''
def _showWebPage(event):
'Show a web page when the user presses the "show" button'
@@ -5173,36 +5184,180 @@ def _showWebPage(event):
txt = event.GetEventObject().page
tmp = tempfile.NamedTemporaryFile(suffix='.html',delete=False)
with open(tmp.name,'w') as fp:
- fp.write(txt.replace('
',' ',))
+ fp.write(txt.replace('',' ',))
fileList.append(tmp.name)
G2G.ShowWebPage('file://'+tmp.name,G2frame)
+
def showWebtext(txt):
import tempfile
tmp = tempfile.NamedTemporaryFile(suffix='.html',delete=False)
with open(tmp.name,'w') as fp:
- fp.write(txt.replace('',' ',))
+ fp.write(txt.replace('',' ',))
fileList.append(tmp.name)
G2G.ShowWebPage('file://'+tmp.name,G2frame)
+ def _get_opt_val(opt_name, out):
+ opt_pattern = rf'NAME="{opt_name}" VALUE="(.*?)"'
+ opt_match = re.search(opt_pattern, out)
+
+ return opt_match.group(1)
+
+ def grab_all_kvecs(out_html):
+ """Extract all k-vectors from the ISODISTORT output HTML."""
+ import re
+ from k_vec_solve import k_vec_solve as kvsolve
+
+ kvec1_pattern = r'(.*?) '
+ kvec1_match = re.search(kvec1_pattern, out_html, re.DOTALL)
+
+ if kvec1_match:
+ select_content = kvec1_match.group(1)
+
+ # Extract option values
+ option_pattern = r']*>([^<]*) '
+ options = re.findall(option_pattern, select_content)
+
+ final_kvec_keys = []
+ for value, _ in options:
+ final_kvec_keys.append(value)
+
+ all_kvecs = {}
+ for key in final_kvec_keys:
+ pattern_str = f"({key.split('(')[1]}"
+ k_form = kvsolve.parse_expression_string(pattern_str)
+ all_kvecs[key] = k_form
+
+ return all_kvecs
+ else:
+ return None
+
+ a, b, g = symbols('a b g')
+
+ def frac_str(value, max_den=1000):
+ # Try to get a rational exactly; if huge, fall back to bounded approximation
+ try:
+ rat = nsimplify(value, rational=True, maxsteps=50)
+ if isinstance(rat, SRational):
+ num, den = rat.as_numer_denom()
+ num, den = int(num), int(den)
+ if den <= max_den:
+ return f"{num}/{den}" if den != 1 else str(num)
+ except Exception:
+ pass
+
+ # Best rational with denominator <= max_den
+ try:
+ f = Fraction(value).limit_denominator(max_den)
+ except TypeError:
+ f = Fraction(float(value)).limit_denominator(max_den)
+
+ return f"{f.numerator}/{f.denominator}" if f.denominator != 1 else str(f.numerator)
+
+ def to_fraction_strs(d, keys=(a, b, g), max_den=1000):
+ out = {}
+ for k in keys:
+ if k in d:
+ out[str(k)] = frac_str(d[k], max_den)
+ return out
+
+ def setup_kvec_input(k_vec, k_vec_dict, isocif_cif):
+ """Set up the input for isodistort post request
+
+ Args:
+ k_vec (str): The k-vector to use for the isodistort request.
+ k_vec_dict (dict): The dictionary containing the k-vector
+ form extracted from isodistort.
+ isocif_cif (str): The CIF file content exported from ISOCIF.
+
+ Returns:
+ dict: New entries and those need to be corrected in the data
+ to be used in the post request.
+ """
+ from k_vec_solve import k_vec_solve as kvsolve
+ k_forms = k_vec_dict.items()
+ all_keys = list(k_forms)
+
+ spg_num = kvsolve.grab_spg_num(isocif_cif)
+ k_vec_sol = kvsolve.find_kvec_form_param(spg_num, isocif_cif, k_vec, k_forms)
+ k_vec_form = all_keys[k_vec_sol[0]]
+
+ data_update = dict()
+ data_update['kvec1'] = k_vec_form[0]
+ k_vec_params = to_fraction_strs(k_vec_sol[1], max_den=1000)
+
+ if "a" in k_vec_params:
+ data_update['kparam11'] = k_vec_params["a"]
+ if "b" in k_vec_params:
+ data_update['kparam21'] = k_vec_params["b"]
+ if "g" in k_vec_params:
+ data_update['kparam31'] = k_vec_params["g"]
+
+ return data_update
+
+ # start of OnISODISTORT_kvec computations
+ if symbols is None:
+ G2G.G2MessageBox(G2frame,
+ 'Unable to perform ISODISTORT kvec search without the sympy module. Use Help/Add packages... to address','No sympy')
+ return
+ try:
+ import requests
+ except:
+ G2G.G2MessageBox(G2frame,
+ 'Unable to perform ISODISTORT kvec search without the requests module. Use Help/Add packages... to address','No requests')
+ return
import tempfile
import re
- import requests
- from exports import G2export_CIF
+ from GSASII.exports import G2export_CIF
from . import ISODISTORT as ISO
- isoformsite = 'https://iso.byu.edu/iso/isodistortform.php'
+ isoformsite = 'https://iso.byu.edu/isodistortform.php'
+ isocifformsite = 'https://iso.byu.edu/isocifform.php'
+ isocifuploadsite = 'https://iso.byu.edu/isocifuploadfile.php'
+
+ if not G2frame.kvecSearch['mode']:
+ return
+
+ k_table = G2frame.GPXtree.GetItemPyData(UnitCellsId)
+ k_cells, _ = k_table[2:4]
+ kpoint = None
+ for row in range(len(k_cells)):
+ if UnitCellsTable.GetValue(row, 0):
+ kpoint = cells[row][3:6]
+ break
+
+ if kpoint is None:
+ wx.MessageBox(
+ "Please select a k-vector from the table.",
+ style=wx.ICON_INFORMATION,
+ caption='Isotropic Subgroup Generation'
+ )
+
+ return
+
+ isoCite = G2G.GetCite('ISOTROPY, ISODISTORT, ISOCIF...',wrap=60,indent=5) # reuse saved citation
- #isoscript='isocifform.php'
- #isoCite = ('For use of this please cite\n'+
- # G2G.GetCite('ISOTROPY, ISODISTORT, ISOCIF...',wrap=60,indent=5)+
- # G2G.GetCite('ISODISPLACE',wrap=60,indent=5))
+ info_str = '''CIF files of the isotropic subgroups associated with the
+ selected k-vector will be created.
+ Generated CIF files will be saved in the same directory as the
+ current project file.
+ This can take up to a few minutes. Check the terminal for progress.
+ '''
+ wx.MessageBox(
+ f"{isoCite}\n\n{info_str}",
+ style=wx.ICON_INFORMATION,
+ caption='Isotropic Subgroup Generation'
+ )
+
+ wx.GetApp().Yield()
+
+ info_msg = "Processing IRREPs for the selected k-vector. "
+ info_msg += "This can take up to a few minutes."
+ print(info_msg)
- #latTol,coordTol,occTol = 0.001, 0.01, 0.1
+ # find tree item for current phase
phaseID = G2gd.GetGPXtreeItemId(G2frame,G2frame.root,'Phases')
- Phase = G2frame.GPXtree.GetItemPyData(G2gd.GetGPXtreeItemId(
- G2frame,phaseID,phase_nam))
- data = Phase
- #oacomp,occomp = G2mth.phaseContents(data)
- #ophsnam = data['General']['Name']
+ phase_nam = G2frame.kvecSearch['phase']
+ phaseTreeId = G2gd.GetGPXtreeItemId(G2frame, phaseID, phase_nam) # save reference
+ Phase = G2frame.GPXtree.GetItemPyData(phaseTreeId)
fileList = []
# write a CIF as a scratch file
obj = G2export_CIF.ExportPhaseCIF(G2frame)
@@ -5211,8 +5366,8 @@ def showWebtext(txt):
obj.loadTree()
tmp = tempfile.NamedTemporaryFile(suffix='.cif', delete=False)
obj.dirname,obj.filename = os.path.split(tmp.name)
- obj.phasenam = data['General']['Name']
- obj.Writer('', data['General']['Name'])
+ obj.phasenam = Phase['General']['Name']
+ obj.Writer('', Phase['General']['Name'])
parentcif = tmp.name
ISOparentcif = ISO.UploadCIF(parentcif)
up2 = {'filename': ISOparentcif, 'input': 'uploadparentcif'}
@@ -5237,11 +5392,47 @@ def showWebtext(txt):
except ValueError:
break
- # TODO: bring in the searched k-vector.
- # we can use the `use` check box to select the k-vector to use.
+ phase_sel = G2frame.kvecSearch['phase']
+ _, Phases = G2frame.GetUsedHistogramsAndPhasesfromTree()
+ Phase = Phases[phase_sel]
+
data['input'] = 'kvector'
data['irrepcount'] = '1'
- data['kvec1'] = ' 1 *GM, k16 (0,0,0)'
+
+ # We need to upload the CIF file to ISOCIF and export from there, since
+ # some of the routines for k vector form solving only works with the
+ # CIF coming out from ISOCIF.
+ init_cif = ISO.UploadCIF(parentcif, upload_site=isocifuploadsite)
+ isocif_up = {'submit': 'OK', 'input': 'uploadcif', 'filename': init_cif}
+ isocif_out_1 = requests.post(isocifformsite, data=isocif_up).text
+
+ isocif_form = re.split(
+ '")
str_tmp = out3[pos:][:pos1]
- ir_options = re.findall(r'([^<]+) ',str_tmp)
+ ir_options = re.findall(
+ r'([^<]+) ',str_tmp
+ )
+
+ proj_pth = os.path.split(os.path.abspath(G2frame.GSASprojectfile))[0]
+
+ G2frame.OnFileSave(None)
+ orgFilName = G2frame.GSASprojectfile
+ phsnam = phase_sel
+ # get restraints & clear geometrical restraints
+ resId = G2gd.GetGPXtreeItemId(G2frame, G2frame.root, 'Restraints')
+ Restraints = G2frame.GPXtree.GetItemPyData(resId)
+ resId = G2gd.GetGPXtreeItemId(G2frame, resId, phsnam)
+ #savedRestraints = None
+ if phsnam in Restraints:
+ Restraints[phsnam]['Bond']['Bonds'] = []
+ Restraints[phsnam]['Angle']['Angles'] = []
+ #savedRestraints = Restraints[phsnam]
+ del Restraints[phsnam]
+ #orgData = copy.deepcopy(data)
for ir_opt, _ in ir_options:
+ print("Processing irrep:", ir_opt)
data["input"] = "irrep"
data['irrep1'] = ir_opt
out4 = requests.post(isoformsite, data=data).text
@@ -5286,23 +5491,78 @@ def _get_opt_val(opt_name, out):
radio_val_pattern = re.compile(r_pattern, re.IGNORECASE)
radio_vals = radio_val_pattern.findall(out4)
cleaned_radio_vals = [value.strip() for value in radio_vals]
+ iso_fn = _get_opt_val('isofilename', out4).strip()
+ data["isofilename"] = iso_fn
for radio_val in cleaned_radio_vals:
+ print("Processing mode:", radio_val)
data["input"] = "distort"
data["origintype"] = "method2"
data["orderparam"] = radio_val + '" CHECKED'
- data["isofilename"] = ""
- requests.post(isoformsite, data=data).text
+ out5 = requests.post(isoformsite, data=data).text
- continue
+ out_cif = ISO.GetISOcif(out5, 2)
+ cif_fn_part1 = radio_val.split()[0]
+ cif_fn_part2_tmp = radio_val.split(")")[1].split(",")[0]
+ cif_fn_part2 = cif_fn_part2_tmp.split()[-1]
+ cif_fn = f"{phase_nam}_{cif_fn_part1}_{cif_fn_part2}.cif"
+ cif_fn = os.path.join(proj_pth, cif_fn)
+ with open(cif_fn, 'wb') as fl:
+ fl.write(out_cif.encode("utf-8"))
- # TODO: parse out the distortion info from out5
- # 1. download the CIF file for each search result
- # 2. load the CIF file as a phase and create a project for it
- # 3. we may want to package up all the project files and save
- # to a user specified location for later use.
+ try:
+ rdlist = G2sc.import_generic(
+ cif_fn, [CIFpr()], fmthint='CIF'
+ )
+ except Exception:
+ continue
+
+ rd = rdlist[0]
+
+ key_list = [
+ 'General', 'Atoms', 'Drawing',
+ 'Histograms', 'Pawley ref', 'RBModels'
+ ]
+ for key in key_list:
+ Phase[key] = rd.Phase[key]
+
+ newname = rd.Phase['General']['Name']
+ Phase['General']['Name'] = phsnam
+
+ # rename the phase in the data tree
+ G2phsG.renamePhaseName(G2frame,Phase,phaseTreeId,Phase['General'],newname)
+
+ G2frame.GSASprojectfile = os.path.splitext(
+ orgFilName
+ )[0] + '_' f"{phase_nam}_{cif_fn_part1}_{cif_fn_part2}.gpx"
+ G2IO.ProjFileSave(G2frame)
+
+ # restore the original saved project
+ G2frame.OnFileOpen(None, filename=orgFilName, askSave=False)
+
+ # reopen tree to the original phase
+ def _ShowPhase():
+ phId = G2gd.GetGPXtreeItemId(G2frame, G2frame.root, 'Phases')
+ G2frame.GPXtree.Expand(phId)
+ phId = G2gd.GetGPXtreeItemId(G2frame, phId, phsnam)
+ G2frame.GPXtree.SelectItem(phId)
- os.unlink(tmp.name)
+ wx.CallLater(100, _ShowPhase)
+
+ info_msg = f'''Done with subgroup output for the selected k-vector.
+ Please check output files in the following directory,
+ {os.getcwd()}
+ '''
+ wx.MessageBox(
+ info_msg,
+ style=wx.ICON_INFORMATION,
+ caption='Isotropic Subgroup Generation'
+ )
+
+ try:
+ os.unlink(tmp.name)
+ except PermissionError:
+ pass
return
@@ -5310,7 +5570,6 @@ def updateCellsWindow(event):
'called when k-vec mode is selected'
wx.CallAfter(UpdateUnitCellsGrid,G2frame,data)
-
def OnClearCells(event):
'remove previous search results'
data[2] = []
@@ -5389,7 +5648,6 @@ def _onResizeUnitCellsList(event):
event.Skip()
except: # can fail after window is destroyed
pass
-
# Display of Autoindexing controls
def firstSizer():
@@ -5445,6 +5703,7 @@ def kvecSizer():
def OnKvecSearch(event):
'Run the k-vector search'
+ from . import k_vector_search as kvs
try:
import seekpath
@@ -6866,15 +7125,12 @@ def OnRefreshKeep(event):
else:
gridDisplay.SetReadOnly(r,c,isReadOnly=True)
if mode == 2:
- #OnISODISTORT_kvec(phase_sel) # TODO: not ready yet
-
hSizer = wx.BoxSizer(wx.HORIZONTAL)
hSizer.Add(gridDisplay)
- # TODO: Add a button to call ISODISTORT
- # ISObut = wx.Button(G2frame.dataWindow,label='Call ISODISTORT')
- # ISObut.Bind(wx.EVT_BUTTON,OnISODIST)
- # hSizer.Add(ISObut)
+ ISObut = wx.Button(G2frame.dataWindow,label='Call ISODISTORT')
+ ISObut.Bind(wx.EVT_BUTTON, OnISODISTORT_kvec)
+ hSizer.Add(ISObut)
mainSizer.Add(hSizer)
else:
@@ -7206,7 +7462,7 @@ def setBackgroundColors(im,it):
def OnToggleExt(event):
G2frame.Hide = not G2frame.Hide
UpdateReflectionGrid(G2frame,data,HKLF=True,Name=Name)
-
+
def OnPageChanged(event):
'''Respond to a press on a phase tab by displaying the reflections. This
routine is needed because the reflection table may not have been created yet.
diff --git a/GSASII/ISODISTORT.py b/GSASII/ISODISTORT.py
index e28a5d62..275eac92 100644
--- a/GSASII/ISODISTORT.py
+++ b/GSASII/ISODISTORT.py
@@ -11,8 +11,8 @@
from . import GSASIIscriptable as G2sc
from . import GSASIIctrlGUI as G2G
#import tempfile
-isouploadsite = 'https://stokes.byu.edu/iso/isodistortuploadfile.php'
-isoformsite = 'https://iso.byu.edu/iso/isodistortform.php'
+isouploadsite = 'https://iso.byu.edu/isodistortuploadfile.php'
+isoformsite = 'https://iso.byu.edu/isodistortform.php'
def HandleError(out):
with open('out.html','wb') as fp:
@@ -26,11 +26,11 @@ def HandleError(out):
except:
print('Could not open URL')
-def UploadCIF(cifname):
- #upload cif file to BYU web site
+def UploadCIF(cifname, upload_site=isouploadsite):
+ #upload cif file to BYU web site
ciffile = open(cifname,'rb')
up1 = {'toProcess':(cifname,ciffile),}
- out1 = requests.post(isouploadsite,files=up1).text
+ out1 = requests.post(upload_site,files=up1).text
ciffile.close()
#retrieve BYU temp file name for cif file
@@ -237,6 +237,8 @@ def GetISOcif(out4,method):
data3['strainamplitude'] = '0.1'
# for item in data3:
# print(item,data3[item])
+ if 'appbtn' in data3:
+ data3.pop('appbtn')
k = requests.post(isoformsite,data=data3)
out5 = k.text #this is output cif!
#print(out5)
diff --git a/GSASII/exports/G2export_CIF.py b/GSASII/exports/G2export_CIF.py
index e1da3e6b..98e95068 100644
--- a/GSASII/exports/G2export_CIF.py
+++ b/GSASII/exports/G2export_CIF.py
@@ -2544,8 +2544,8 @@ def WritePhaseInfo(phasenam,quick=True,oneblock=True):
self.labellist = []
WriteAtomsNuclear(self.fp, self.Phases[phasenam], phasenam,
self.parmDict, self.sigDict, self.labellist,
- self.OverallParms['Rigid bodies'])
-# self.RBsuDict)
+ self.OverallParms['Rigid bodies'],
+ getattr(self, 'RBsuDict', {}))
else:
try:
self.labellist
diff --git a/GSASII/k_vec_solve/k_vec_solve.py b/GSASII/k_vec_solve/k_vec_solve.py
new file mode 100644
index 00000000..2c5e4e7e
--- /dev/null
+++ b/GSASII/k_vec_solve/k_vec_solve.py
@@ -0,0 +1,332 @@
+# -*- coding: utf-8 -*-
+"""k_vec_solve.py
+Routines for the determination of the k-vector form compatible with ISODISTORT.
+
+Author: Yuanpeng Zhang, with the help from Prof. Branton Campbell and Dr. Brian Toby
+Date: 08/20/2025 11:56:28 EST
+"""
+import re
+import json
+import numpy as np
+from fractions import Fraction
+from sympy import Eq, solve, Matrix, symbols, sympify
+import os
+
+a, b, g = symbols('a b g')
+
+
+def parse_expression_string(expr_string):
+ """
+ Parse a string like '(a+1/2, 2b/3, g/3+2/3)' into a list of sympy expressions.
+
+ Args:
+ expr_string (str): String containing comma-separated expressions in parentheses
+
+ Returns:
+ list: List of sympy expressions
+ """
+ clean_string = expr_string.strip('()')
+ expressions = [expr.strip() for expr in clean_string.split(',')]
+
+ sympy_expressions = []
+ for expr in expressions:
+ expr_with_mult = re.sub(r'(\d)([a-zA-Z])', r'\1*\2', expr)
+
+ sympy_expr = sympify(expr_with_mult)
+ sympy_expressions.append(sympy_expr)
+
+ return sympy_expressions
+
+
+def transform_spg_ops_to_matrix(spg_ops, syms):
+ '''Transforming space group operators in the string form into a matrix.
+
+ Args:
+ spg_ops (list): A list of operators list like ["-x + y + 1/2", "-x", "z"]
+ syms (list): A list of symbols corresponding to the operators
+
+ Returns:
+ numpy.ndarray: A numpy array of space group operator matrices.
+ '''
+ base_vectors = {
+ syms[0]: [1, 0, 0],
+ syms[1]: [0, 1, 0],
+ syms[2]: [0, 0, 1],
+ }
+
+ matrices = []
+
+ def parse_element(element):
+ resulatt_type_vector = [0, 0, 0]
+ element = element.replace(' ', '')
+ terms = re.split('(?=[+-])', element)
+
+ for term in terms:
+ if syms[0] in term:
+ sign = -1 if term.startswith('-') else 1
+ resulatt_type_vector = [rv + sign * bv for rv, bv in zip(resulatt_type_vector, base_vectors[syms[0]])]
+ elif syms[1] in term:
+ sign = -1 if term.startswith('-') else 1
+ resulatt_type_vector = [rv + sign * bv for rv, bv in zip(resulatt_type_vector, base_vectors[syms[1]])]
+ elif syms[2] in term:
+ sign = -1 if term.startswith('-') else 1
+ resulatt_type_vector = [rv + sign * bv for rv, bv in zip(resulatt_type_vector, base_vectors[syms[2]])]
+
+ return resulatt_type_vector
+
+ def extract_numeric_part(expression):
+ numeric_pattern = r'[-]?\d+\/\d+|\d+\.\d+|\d+'
+ numeric_parts = re.findall(numeric_pattern, expression)
+
+ return numeric_parts[0] if numeric_parts else '0'
+
+ for operation in spg_ops:
+ matrix = []
+
+ for element in operation:
+ vector = [float(item) for item in parse_element(element)]
+ num_part = float(Fraction(extract_numeric_part(element)))
+ vector.append(num_part)
+ matrix.append(vector)
+
+ matrix.append([0, 0, 0, 1])
+ matrix_a = np.array(matrix).T
+ matrices.append(matrix_a)
+
+ return np.array(matrices)
+
+
+def grab_user_conv_transform(trans_str):
+ """Given the transformation string from the space group unit cell setting to
+ the conventional setting, we want to figure out the transformation matrix.
+
+ Args:
+ trans_str (str): transformation string from a CIF file with the key of '_space_group.transform_Pp_abc'
+
+ Returns:
+ numpy.ndarray: A numpy array of the transformation matrix.
+ """
+ x_op_1 = trans_str.split(";")[0].split(",")[0]
+ x_op_2 = trans_str.split(";")[1].split(",")[0]
+ if float(x_op_2) >= 0.:
+ x_op_2 = f"+ {x_op_2}"
+ x_op = x_op_1 + x_op_2
+
+ y_op_1 = trans_str.split(";")[0].split(",")[1]
+ y_op_2 = trans_str.split(";")[1].split(",")[1]
+ if float(y_op_2) >= 0.:
+ y_op_2 = f"+ {y_op_2}"
+ y_op = y_op_1 + y_op_2
+
+ z_op_1 = trans_str.split(";")[0].split(",")[2]
+ z_op_2 = trans_str.split(";")[1].split(",")[2]
+ if float(z_op_2) >= 0.:
+ z_op_2 = f"+ {z_op_2}"
+ z_op = z_op_1 + z_op_2
+
+ op_str = [[x_op, y_op, z_op]]
+
+ syms = ['a', 'b', 'c']
+ user_to_conv = transform_spg_ops_to_matrix(op_str, syms)[0]
+
+ return user_to_conv
+
+
+def grab_spg_num(cif_contents):
+ """Grab the space group number from the '_symmetry_Int_Tables_number' line in a given CIF file.
+
+ Args:
+ cif_contents (str): Contents of the CIF file.
+
+ Returns:
+ str: The space group number, or None if not found.
+ """
+ spg_num = None
+ lines = cif_contents.splitlines()
+ for line in lines:
+ if '_symmetry_Int_Tables_number' in line:
+ parts = line.split()
+ if len(parts) > 1:
+ spg_num = parts[1]
+ break
+
+ return spg_num
+
+
+def grab_user_conv_line(cif_contents):
+ """Grab the user to conventional setting transformation from the
+ '_space_group.transform_Pp_abc' line in a given CIF file.
+
+ Args:
+ cif_contents (str): Contents of the CIF file.
+
+ Returns:
+ str: The user to conventional setting transformation string, or None if not found.
+ """
+ trans_str = None
+ lines = cif_contents.splitlines()
+ for line in lines:
+ if '_space_group.transform_Pp_abc' in line:
+ parts = line.split()
+ if len(parts) > 1:
+ trans_str = parts[1].strip()
+ break
+
+ return trans_str
+
+
+def latt_prim_bases_ext(latt_type):
+ """Prime lattice basis for a given lattice type.
+
+ Args:
+ latt_type (str): Lattice type
+
+ Returns:
+ list: Prime lattice basis
+ """
+ if latt_type == "A":
+ lp_matrix = np.array([[1, 0, 0], [0, 1/2, 1/2], [0, -1/2, 1/2]])
+ elif latt_type == "B":
+ lp_matrix = np.array([[1/2, 0, -1/2], [0, 1, 0], [1/2, 0, 1/2]])
+ elif latt_type == "C":
+ lp_matrix = np.array([[1/2, 1/2, 0], [-1/2, 1/2, 0], [0, 0, 1]])
+ elif latt_type == "F":
+ lp_matrix = np.array([[0, 1/2, 1/2], [1/2, 0, 1/2], [1/2, 1/2, 0]])
+ elif latt_type == "I":
+ lp_matrix = np.array([[-1/2, 1/2, 1/2], [1/2, -1/2, 1/2], [1/2, 1/2, -1/2]])
+ elif latt_type == "R":
+ lp_matrix = np.array([[2/3, 1/3, 1/3], [-1/3, 1/3, 1/3], [-1/3, -2/3, 1/3]])
+ else:
+ lp_matrix = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+
+ lp_matrix_t = lp_matrix.T
+ lp_matrix_ext = np.hstack((lp_matrix_t, np.zeros((lp_matrix_t.shape[0], 1))))
+ lp_matrix_ext = np.vstack((lp_matrix_ext, np.array([0, 0, 0, 1])))
+
+ return lp_matrix_ext
+
+
+def solve_kvec_params(numkvec, kform):
+ """Given input k vector and the alternative k vector form, try to
+ solve the parameters associated with the provided form.
+
+ Args:
+ numkvec (list): k vector
+ kform (numpy array): Candidate k vector form
+
+ Returns:
+ list or dict: Solution for parameters involved in the provided k vector form.
+ If a solution is found, the return will be a dictionary with parameter names as keys and their
+ corresponding values as dict values. If no solution is found, an empty list is returned.
+ """
+ # Convert to sympy Matrix
+ kform_m = Matrix(kform)
+
+ # Check if kform contains only numbers
+ if not kform_m.free_symbols:
+ # Perform a piecewise comparison
+ kform_f = [float(f) for f in kform]
+ if all(n == f for n, f in zip(numkvec, kform_f)):
+ return {'match': True}
+ else:
+ return {'match': False}
+
+ # If kform contains symbols, solve for the parameters
+ kvars = list(kform_m.free_symbols)
+ kequats = [Eq(kform_m[i] - n, 0) for i, n in enumerate(numkvec)]
+ ksols = solve(kequats, kvars)
+
+ return ksols
+
+
+def find_kvec_form_param(spg_num, isocif_cif, k_vec, k_forms):
+ """Find the parameters for a given k vector form.
+
+ Args:
+ spg_num (int): Space group number.
+ isocif_cif (str): Contents of the CIF file exported from ISOCIF.
+ k_vec (list): k vector
+ k_forms (list): List of symbolic alternative k vector forms.
+ Entries should be in the form of sympy expressions.
+
+ Returns:
+ tuple: (index of k_form, a, b, g)
+ """
+ script_path = os.path.dirname(os.path.abspath(__file__))
+ with open(os.path.join(script_path, "sgtables.json"), "r") as f:
+ sgtables = json.load(f)
+
+ spg_sym = sgtables[str(spg_num)]["SPGSym"]
+ user_aff_ops = transform_spg_ops_to_matrix(
+ sgtables[str(spg_num)]["SPGOps"],
+ syms=['x', 'y', 'z']
+ )
+
+ user_to_ref_conv_p_l = grab_user_conv_line(isocif_cif)
+ user_to_ref_conv_p = grab_user_conv_transform(user_to_ref_conv_p_l)
+ user_to_ref_conv_q = np.linalg.inv(user_to_ref_conv_p)
+
+ conv_to_pr_p = latt_prim_bases_ext(spg_sym[0])
+ conv_to_pr_q = np.linalg.inv(conv_to_pr_p)
+
+ user_to_ref_pr_q = np.dot(conv_to_pr_q, user_to_ref_conv_q)
+ user_to_ref_pr_p = np.linalg.inv(user_to_ref_pr_q)
+
+ ref_pt_ops = np.matmul(user_to_ref_pr_q, np.matmul(user_aff_ops, user_to_ref_pr_p))
+
+ k_vec_pr = np.dot(np.array(k_vec), user_to_ref_pr_p[0:3, 0:3])
+ k_forms_tmp = []
+ for k_form_t in k_forms:
+ k_forms_tmp.append(k_form_t[1])
+ k_forms_tmp = np.array(k_forms_tmp)
+ k_forms_pr = np.matmul(k_forms_tmp, user_to_ref_pr_p[0:3, 0:3])
+
+ def sort_keys(dict_entry):
+ # Sort keys by priority: a, then b, then g
+ key_priority = {a: 1, b: 2, g: 3}
+ return [key_priority.get(key, float('inf')) for key in dict_entry]
+
+ k_vec_pr_arms = np.matmul(k_vec_pr, ref_pt_ops[0:3, 0:3])
+ alt_solutions = []
+ for arm in k_vec_pr_arms:
+ arm_sols = []
+ for k_form in k_forms_pr:
+ sol = solve_kvec_params(arm[:3], k_form)
+ if sol:
+ arm_sols.append(sol)
+ else:
+ arm_sols.append(None)
+
+ min_keys = float('inf')
+ best_dict = None
+ best_index = -1
+
+ for i, entry in enumerate(arm_sols):
+ if isinstance(entry, dict):
+ if 'match' in entry and entry['match'] is True:
+ num_keys = 0
+ else:
+ num_keys = len(entry)
+
+ # Compare this entry to the current best entry
+ if num_keys < min_keys or (num_keys == min_keys and sort_keys(entry) < sort_keys(best_dict)):
+ min_keys = num_keys
+ best_dict = entry
+ best_index = i
+
+ alt_solutions.append([best_index, min_keys, best_dict])
+
+ min_keys = float('inf')
+ best_dict = None
+ best_index = -1
+
+ for entry in alt_solutions:
+ if entry[0] != -1:
+ num_keys = entry[1]
+
+ if num_keys < min_keys or (num_keys == min_keys and sort_keys(entry[2]) < sort_keys(best_dict)):
+ min_keys = num_keys
+ best_dict = entry[2]
+ best_index = entry[0]
+
+ return (best_index, best_dict)
diff --git a/GSASII/k_vec_solve/sgtables.json b/GSASII/k_vec_solve/sgtables.json
new file mode 100644
index 00000000..1d66bdc4
--- /dev/null
+++ b/GSASII/k_vec_solve/sgtables.json
@@ -0,0 +1,14149 @@
+{
+ "1":{
+ "SPGSym":"P1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ]
+ ]
+ },
+ "2":{
+ "SPGSym":"P-1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ]
+ ]
+ },
+ "3":{
+ "SPGSym":"P2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "4":{
+ "SPGSym":"P2_1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "-z"
+ ]
+ ]
+ },
+ "5":{
+ "SPGSym":"C2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "6":{
+ "SPGSym":"Pm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "7":{
+ "SPGSym":"Pc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "8":{
+ "SPGSym":"Cm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "9":{
+ "SPGSym":"Cc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "10":{
+ "SPGSym":"P2\/m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "11":{
+ "SPGSym":"P2_1\/m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "z"
+ ]
+ ]
+ },
+ "12":{
+ "SPGSym":"C2\/m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "13":{
+ "SPGSym":"P2\/c",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "14":{
+ "SPGSym":"P2_1\/c",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "15":{
+ "SPGSym":"C2\/c",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "16":{
+ "SPGSym":"P222",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "17":{
+ "SPGSym":"P222_1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "18":{
+ "SPGSym":"P2_12_12",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "19":{
+ "SPGSym":"P2_12_12_1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "20":{
+ "SPGSym":"C222_1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "21":{
+ "SPGSym":"C222",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "22":{
+ "SPGSym":"F222",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "23":{
+ "SPGSym":"I222",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "24":{
+ "SPGSym":"I2_12_12_1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 - y",
+ "z"
+ ]
+ ]
+ },
+ "25":{
+ "SPGSym":"Pmm2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "26":{
+ "SPGSym":"Pmc2_1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "27":{
+ "SPGSym":"Pcc2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "28":{
+ "SPGSym":"Pma2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "29":{
+ "SPGSym":"Pca2_1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "30":{
+ "SPGSym":"Pnc2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "31":{
+ "SPGSym":"Pmn2_1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "32":{
+ "SPGSym":"Pba2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "z"
+ ]
+ ]
+ },
+ "33":{
+ "SPGSym":"Pna2_1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "z"
+ ]
+ ]
+ },
+ "34":{
+ "SPGSym":"Pnn2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "35":{
+ "SPGSym":"Cmm2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "36":{
+ "SPGSym":"Cmc2_1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "37":{
+ "SPGSym":"Ccc2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "38":{
+ "SPGSym":"Amm2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "39":{
+ "SPGSym":"Abm2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "40":{
+ "SPGSym":"Ama2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "41":{
+ "SPGSym":"Aba2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "42":{
+ "SPGSym":"Fmm2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "43":{
+ "SPGSym":"Fdd2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/4 - x",
+ "1\/4 + y",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 - y",
+ "1\/4 + z"
+ ]
+ ]
+ },
+ "44":{
+ "SPGSym":"Imm2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "45":{
+ "SPGSym":"Iba2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "46":{
+ "SPGSym":"Ima2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "z"
+ ]
+ ]
+ },
+ "47":{
+ "SPGSym":"Pmmm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "48":{
+ "SPGSym":"Pnnn",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ]
+ ]
+ },
+ "49":{
+ "SPGSym":"Pccm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "50":{
+ "SPGSym":"Pban",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ]
+ ]
+ },
+ "51":{
+ "SPGSym":"Pmma",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "52":{
+ "SPGSym":"Pnna",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "53":{
+ "SPGSym":"Pmna",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "y",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "54":{
+ "SPGSym":"Pcca",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "55":{
+ "SPGSym":"Pbam",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "56":{
+ "SPGSym":"Pccn",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ]
+ ]
+ },
+ "57":{
+ "SPGSym":"Pbcm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "y",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "58":{
+ "SPGSym":"Pnnm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "59":{
+ "SPGSym":"Pmmn",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ]
+ ]
+ },
+ "60":{
+ "SPGSym":"Pbcn",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "61":{
+ "SPGSym":"Pbca",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "y",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "62":{
+ "SPGSym":"Pnma",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "y",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "63":{
+ "SPGSym":"Cmcm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "y",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "64":{
+ "SPGSym":"Cmca",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "y",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "65":{
+ "SPGSym":"Cmmm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "66":{
+ "SPGSym":"Cccm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "67":{
+ "SPGSym":"Cmma",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "68":{
+ "SPGSym":"Ccca",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "69":{
+ "SPGSym":"Fmmm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "70":{
+ "SPGSym":"Fddd",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "3\/4 - y",
+ "3\/4 - z"
+ ],
+ [
+ "3\/4 - x",
+ "y",
+ "3\/4 - z"
+ ],
+ [
+ "3\/4 - x",
+ "3\/4 - y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/4 + y",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + x",
+ "-y",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 + y",
+ "-z"
+ ]
+ ]
+ },
+ "71":{
+ "SPGSym":"Immm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "72":{
+ "SPGSym":"Ibam",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ]
+ ]
+ },
+ "73":{
+ "SPGSym":"Ibca",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 + y",
+ "-z"
+ ]
+ ]
+ },
+ "74":{
+ "SPGSym":"Imma",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 + y",
+ "-z"
+ ]
+ ]
+ },
+ "75":{
+ "SPGSym":"P4",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ]
+ ]
+ },
+ "76":{
+ "SPGSym":"P4_1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/4 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "3\/4 + z"
+ ]
+ ]
+ },
+ "77":{
+ "SPGSym":"P4_2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "78":{
+ "SPGSym":"P4_3",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x",
+ "3\/4 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/4 + z"
+ ]
+ ]
+ },
+ "79":{
+ "SPGSym":"I4",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ]
+ ]
+ },
+ "80":{
+ "SPGSym":"I4_1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "1\/4 + z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "1\/4 + z"
+ ]
+ ]
+ },
+ "81":{
+ "SPGSym":"P-4",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ]
+ ]
+ },
+ "82":{
+ "SPGSym":"I-4",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ]
+ ]
+ },
+ "83":{
+ "SPGSym":"P4\/m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ]
+ ]
+ },
+ "84":{
+ "SPGSym":"P4_2\/m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "85":{
+ "SPGSym":"P4\/n",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/2 + y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "-z"
+ ]
+ ]
+ },
+ "86":{
+ "SPGSym":"P4_2\/n",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "x",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "87":{
+ "SPGSym":"I4\/m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ]
+ ]
+ },
+ "88":{
+ "SPGSym":"I4_1\/a",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "3\/4 - y",
+ "1\/4 + x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 - x",
+ "1\/4 + z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/4 + y",
+ "3\/4 - x",
+ "3\/4 - z"
+ ],
+ [
+ "3\/4 - y",
+ "3\/4 + x",
+ "3\/4 - z"
+ ]
+ ]
+ },
+ "89":{
+ "SPGSym":"P422",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ]
+ ]
+ },
+ "90":{
+ "SPGSym":"P42_12",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ]
+ ]
+ },
+ "91":{
+ "SPGSym":"P4_122",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/4 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "3\/4 + z"
+ ],
+ [
+ "y",
+ "x",
+ "3\/4 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/4 - z"
+ ]
+ ]
+ },
+ "92":{
+ "SPGSym":"P4_12_12",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "3\/4 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/4 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "3\/4 + z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "93":{
+ "SPGSym":"P4_222",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "94":{
+ "SPGSym":"P4_22_12",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ]
+ ]
+ },
+ "95":{
+ "SPGSym":"P4_322",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x",
+ "3\/4 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/4 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/4 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "3\/4 - z"
+ ]
+ ]
+ },
+ "96":{
+ "SPGSym":"P4_32_12",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/4 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "3\/4 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "3\/4 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "1\/4 + z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "97":{
+ "SPGSym":"I422",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ]
+ ]
+ },
+ "98":{
+ "SPGSym":"I4_122",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/4 - z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/4 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "1\/4 + z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "1\/4 + z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ]
+ ]
+ },
+ "99":{
+ "SPGSym":"P4mm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "100":{
+ "SPGSym":"P4bm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "z"
+ ]
+ ]
+ },
+ "101":{
+ "SPGSym":"P4_2cm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "102":{
+ "SPGSym":"P4_2nm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "103":{
+ "SPGSym":"P4cc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "104":{
+ "SPGSym":"P4nc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "105":{
+ "SPGSym":"P4_2mc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "106":{
+ "SPGSym":"P4_2bc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "107":{
+ "SPGSym":"I4mm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "108":{
+ "SPGSym":"I4cm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "109":{
+ "SPGSym":"I4_1md",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "1\/4 + z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "1\/4 + z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "1\/2 - x",
+ "1\/4 + z"
+ ],
+ [
+ "y",
+ "1\/2 + x",
+ "1\/4 + z"
+ ]
+ ]
+ },
+ "110":{
+ "SPGSym":"I4_1cd",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "1\/4 + z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "1\/4 + z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 - y",
+ "-x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/2 + y",
+ "x",
+ "1\/4 + z"
+ ]
+ ]
+ },
+ "111":{
+ "SPGSym":"P-42m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "112":{
+ "SPGSym":"P-42c",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "113":{
+ "SPGSym":"P-42_1m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "z"
+ ]
+ ]
+ },
+ "114":{
+ "SPGSym":"P-42_1c",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "115":{
+ "SPGSym":"P-4m2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ]
+ ]
+ },
+ "116":{
+ "SPGSym":"P-4c2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ]
+ ]
+ },
+ "117":{
+ "SPGSym":"P-4b2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "-z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ]
+ ]
+ },
+ "118":{
+ "SPGSym":"P-4n2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ]
+ ]
+ },
+ "119":{
+ "SPGSym":"I-4m2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ]
+ ]
+ },
+ "120":{
+ "SPGSym":"I-4c2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ]
+ ]
+ },
+ "121":{
+ "SPGSym":"I-42m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "122":{
+ "SPGSym":"I-42d",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/4 - z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/4 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "1\/2 - x",
+ "1\/4 + z"
+ ],
+ [
+ "y",
+ "1\/2 + x",
+ "1\/4 + z"
+ ]
+ ]
+ },
+ "123":{
+ "SPGSym":"P4\/mmm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "124":{
+ "SPGSym":"P4\/mcc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "125":{
+ "SPGSym":"P4\/nbm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/2 + y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "z"
+ ]
+ ]
+ },
+ "126":{
+ "SPGSym":"P4\/nnc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/2 + y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "127":{
+ "SPGSym":"P4\/mbm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "-z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "z"
+ ]
+ ]
+ },
+ "128":{
+ "SPGSym":"P4\/mnc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "129":{
+ "SPGSym":"P4\/nmm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/2 + y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "-z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "130":{
+ "SPGSym":"P4\/ncc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/2 + y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "-z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "131":{
+ "SPGSym":"P4_2\/mmc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "132":{
+ "SPGSym":"P4_2\/mcm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "133":{
+ "SPGSym":"P4_2\/nbc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/2 + y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "134":{
+ "SPGSym":"P4_2\/nnm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/2 + y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "z"
+ ]
+ ]
+ },
+ "135":{
+ "SPGSym":"P4_2\/mbc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "136":{
+ "SPGSym":"P4_2\/mnm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "137":{
+ "SPGSym":"P4_2\/nmc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/2 + y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "138":{
+ "SPGSym":"P4_2\/ncm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/2 - y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "1\/2 + y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "139":{
+ "SPGSym":"I4\/mmm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "140":{
+ "SPGSym":"I4\/mcm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "141":{
+ "SPGSym":"I4_1\/amd",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/4 - y",
+ "3\/4 + x",
+ "1\/4 + z"
+ ],
+ [
+ "3\/4 + y",
+ "3\/4 - x",
+ "1\/4 + z"
+ ],
+ [
+ "3\/4 + y",
+ "1\/4 + x",
+ "3\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 - x",
+ "3\/4 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "3\/4 + y",
+ "1\/4 - x",
+ "3\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 + x",
+ "3\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "3\/4 - x",
+ "1\/4 + z"
+ ],
+ [
+ "3\/4 + y",
+ "3\/4 + x",
+ "1\/4 + z"
+ ]
+ ]
+ },
+ "142":{
+ "SPGSym":"I4_1\/acd",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "1\/4 - y",
+ "3\/4 + x",
+ "1\/4 + z"
+ ],
+ [
+ "3\/4 + y",
+ "3\/4 - x",
+ "1\/4 + z"
+ ],
+ [
+ "3\/4 + y",
+ "1\/4 + x",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 - x",
+ "1\/4 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "3\/4 + y",
+ "1\/4 - x",
+ "3\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 + x",
+ "3\/4 - z"
+ ],
+ [
+ "3\/4 - y",
+ "1\/4 - x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 + x",
+ "1\/4 + z"
+ ]
+ ]
+ },
+ "143":{
+ "SPGSym":"P3",
+ "SPGOps":[
+ "{x, y, z}",
+ "{-y, x - y, z}",
+ "{-x + y, -x, z}"
+ ]
+ },
+ "144":{
+ "SPGSym":"P3_1",
+ "SPGOps":[
+ "{x, y, z}",
+ "{-y, x - y, 1\/3 + z}",
+ "{-x + y, -x, 2\/3 + z}"
+ ]
+ },
+ "145":{
+ "SPGSym":"P3_2",
+ "SPGOps":[
+ "{x, y, z}",
+ "{-y, x - y, 2\/3 + z}",
+ "{-x + y, -x, 1\/3 + z}"
+ ]
+ },
+ "146":{
+ "SPGSym":"R3",
+ "SPGOps":[
+ "{x, y, z}",
+ "{-y, x - y, z}",
+ "{-x + y, -x, z}"
+ ]
+ },
+ "147":{
+ "SPGSym":"P-3",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ]
+ ]
+ },
+ "148":{
+ "SPGSym":"R-3",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ]
+ ]
+ },
+ "149":{
+ "SPGSym":"P312",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ]
+ ]
+ },
+ "150":{
+ "SPGSym":"P321",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "-z"
+ ]
+ ]
+ },
+ "151":{
+ "SPGSym":"P3_112",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "1\/3 + z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "2\/3 + z"
+ ],
+ [
+ "x",
+ "x - y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/3 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "2\/3 - z"
+ ]
+ ]
+ },
+ "152":{
+ "SPGSym":"P3_121",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "1\/3 + z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "2\/3 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "2\/3 - z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/3 - z"
+ ]
+ ]
+ },
+ "153":{
+ "SPGSym":"P3_212",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "2\/3 + z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "1\/3 + z"
+ ],
+ [
+ "x",
+ "x - y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "2\/3 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/3 - z"
+ ]
+ ]
+ },
+ "154":{
+ "SPGSym":"P3_221",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "2\/3 + z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "1\/3 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "1\/3 - z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "2\/3 - z"
+ ]
+ ]
+ },
+ "155":{
+ "SPGSym":"R32",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "-z"
+ ]
+ ]
+ },
+ "156":{
+ "SPGSym":"P3m1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "z"
+ ]
+ ]
+ },
+ "157":{
+ "SPGSym":"P31m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "158":{
+ "SPGSym":"P3c1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "159":{
+ "SPGSym":"P31c",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/2 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "160":{
+ "SPGSym":"R3m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "z"
+ ]
+ ]
+ },
+ "161":{
+ "SPGSym":"R3c",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "162":{
+ "SPGSym":"P-31m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "163":{
+ "SPGSym":"P-31c",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/2 - z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/2 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "164":{
+ "SPGSym":"P-3m1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "z"
+ ]
+ ]
+ },
+ "165":{
+ "SPGSym":"P-3c1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "166":{
+ "SPGSym":"R-3m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "z"
+ ]
+ ]
+ },
+ "167":{
+ "SPGSym":"R-3c",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "168":{
+ "SPGSym":"P6",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "z"
+ ]
+ ]
+ },
+ "169":{
+ "SPGSym":"P6_1",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "1\/3 + z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "2\/3 + z"
+ ],
+ [
+ "x - y",
+ "x",
+ "1\/6 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "5\/6 + z"
+ ]
+ ]
+ },
+ "170":{
+ "SPGSym":"P6_5",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "2\/3 + z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "1\/3 + z"
+ ],
+ [
+ "x - y",
+ "x",
+ "5\/6 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "1\/6 + z"
+ ]
+ ]
+ },
+ "171":{
+ "SPGSym":"P6_2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "2\/3 + z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "1\/3 + z"
+ ],
+ [
+ "x - y",
+ "x",
+ "1\/3 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "2\/3 + z"
+ ]
+ ]
+ },
+ "172":{
+ "SPGSym":"P6_4",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "1\/3 + z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "2\/3 + z"
+ ],
+ [
+ "x - y",
+ "x",
+ "2\/3 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "1\/3 + z"
+ ]
+ ]
+ },
+ "173":{
+ "SPGSym":"P6_3",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "174":{
+ "SPGSym":"P-6",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "-z"
+ ]
+ ]
+ },
+ "175":{
+ "SPGSym":"P6\/m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "-z"
+ ]
+ ]
+ },
+ "176":{
+ "SPGSym":"P6_3\/m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "177":{
+ "SPGSym":"P622",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x",
+ "x - y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ]
+ ]
+ },
+ "178":{
+ "SPGSym":"P6_122",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "1\/3 + z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "2\/3 + z"
+ ],
+ [
+ "x - y",
+ "x",
+ "1\/6 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "5\/6 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/3 - z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "2\/3 - z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/6 - z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "5\/6 - z"
+ ]
+ ]
+ },
+ "179":{
+ "SPGSym":"P6_522",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "2\/3 + z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "1\/3 + z"
+ ],
+ [
+ "x - y",
+ "x",
+ "5\/6 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "1\/6 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "2\/3 - z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/3 - z"
+ ],
+ [
+ "x",
+ "x - y",
+ "5\/6 - z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/6 - z"
+ ]
+ ]
+ },
+ "180":{
+ "SPGSym":"P6_222",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "2\/3 + z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "1\/3 + z"
+ ],
+ [
+ "x - y",
+ "x",
+ "1\/3 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "2\/3 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "2\/3 - z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/3 - z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/3 - z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "2\/3 - z"
+ ]
+ ]
+ },
+ "181":{
+ "SPGSym":"P6_422",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "1\/3 + z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "2\/3 + z"
+ ],
+ [
+ "x - y",
+ "x",
+ "2\/3 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "1\/3 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/3 - z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "2\/3 - z"
+ ],
+ [
+ "x",
+ "x - y",
+ "2\/3 - z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/3 - z"
+ ]
+ ]
+ },
+ "182":{
+ "SPGSym":"P6_322",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "1\/2 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/2 - z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ]
+ ]
+ },
+ "183":{
+ "SPGSym":"P6mm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "184":{
+ "SPGSym":"P6cc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/2 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "185":{
+ "SPGSym":"P6_3cm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "1\/2 + z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "186":{
+ "SPGSym":"P6_3mc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "1\/2 + z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/2 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "187":{
+ "SPGSym":"P-6m2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "z"
+ ]
+ ]
+ },
+ "188":{
+ "SPGSym":"P-6c2",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "1\/2 - z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "189":{
+ "SPGSym":"P-62m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "190":{
+ "SPGSym":"P-62c",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/2 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "191":{
+ "SPGSym":"P6\/mmm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x",
+ "x - y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "192":{
+ "SPGSym":"P6\/mcc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/2 - z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/2 - z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/2 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "193":{
+ "SPGSym":"P6_3\/mcm",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "1\/2 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/2 - z"
+ ],
+ [
+ "x",
+ "x - y",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "1\/2 - z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/2 + z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ]
+ ]
+ },
+ "194":{
+ "SPGSym":"P6_3\/mmc",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "-x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "z"
+ ],
+ [
+ "x - y",
+ "x",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "1\/2 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "-z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x",
+ "x - y",
+ "1\/2 - z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "y",
+ "-x + y",
+ "-z"
+ ],
+ [
+ "x - y",
+ "x",
+ "-z"
+ ],
+ [
+ "-x + y",
+ "-x",
+ "1\/2 - z"
+ ],
+ [
+ "-y",
+ "x - y",
+ "1\/2 - z"
+ ],
+ [
+ "-x + y",
+ "y",
+ "z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "x",
+ "x - y",
+ "z"
+ ],
+ [
+ "-x",
+ "-x + y",
+ "1\/2 + z"
+ ],
+ [
+ "x - y",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 + z"
+ ]
+ ]
+ },
+ "195":{
+ "SPGSym":"P23",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ]
+ ]
+ },
+ "196":{
+ "SPGSym":"F23",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ]
+ ]
+ },
+ "197":{
+ "SPGSym":"I23",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ]
+ ]
+ },
+ "198":{
+ "SPGSym":"P2_13",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "1\/2 + z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "-x",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 - y",
+ "-z",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 - x",
+ "-y"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/2 + x",
+ "1\/2 - y"
+ ]
+ ]
+ },
+ "199":{
+ "SPGSym":"I2_13",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "1\/2 - y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/2 - x",
+ "y"
+ ],
+ [
+ "-y",
+ "1\/2 - z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "1\/2 - y"
+ ],
+ [
+ "y",
+ "-z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "x",
+ "-y"
+ ]
+ ]
+ },
+ "200":{
+ "SPGSym":"Pm-3",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "x",
+ "-y"
+ ],
+ [
+ "y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "y"
+ ],
+ [
+ "-y",
+ "z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "y"
+ ]
+ ]
+ },
+ "201":{
+ "SPGSym":"Pn-3",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "1\/2 - y",
+ "z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 - x",
+ "y"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - z",
+ "x"
+ ],
+ [
+ "z",
+ "1\/2 - x",
+ "1\/2 - y"
+ ],
+ [
+ "y",
+ "1\/2 - z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "x",
+ "1\/2 - y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "1\/2 + y",
+ "-z",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 + x",
+ "-y"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/2 + x",
+ "1\/2 + y"
+ ],
+ [
+ "-y",
+ "1\/2 + z",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "-x",
+ "1\/2 + y"
+ ]
+ ]
+ },
+ "202":{
+ "SPGSym":"Fm-3",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "x",
+ "-y"
+ ],
+ [
+ "y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "y"
+ ],
+ [
+ "-y",
+ "z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "y"
+ ]
+ ]
+ },
+ "203":{
+ "SPGSym":"Fd-3",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "3\/4 - y",
+ "3\/4 - z"
+ ],
+ [
+ "3\/4 - x",
+ "y",
+ "3\/4 - z"
+ ],
+ [
+ "3\/4 - x",
+ "3\/4 - y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "3\/4 - y",
+ "z",
+ "3\/4 - x"
+ ],
+ [
+ "3\/4 - z",
+ "3\/4 - x",
+ "y"
+ ],
+ [
+ "3\/4 - y",
+ "3\/4 - z",
+ "x"
+ ],
+ [
+ "z",
+ "3\/4 - x",
+ "3\/4 - y"
+ ],
+ [
+ "y",
+ "3\/4 - z",
+ "3\/4 - x"
+ ],
+ [
+ "3\/4 - z",
+ "x",
+ "3\/4 - y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/4 + y",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + x",
+ "-y",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 + y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "1\/4 + y",
+ "-z",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 + z",
+ "1\/4 + x",
+ "-y"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 + z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/4 + x",
+ "1\/4 + y"
+ ],
+ [
+ "-y",
+ "1\/4 + z",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 + z",
+ "-x",
+ "1\/4 + y"
+ ]
+ ]
+ },
+ "204":{
+ "SPGSym":"Im-3",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "x",
+ "-y"
+ ],
+ [
+ "y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "y"
+ ],
+ [
+ "-y",
+ "z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "y"
+ ]
+ ]
+ },
+ "205":{
+ "SPGSym":"Pa-3",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "1\/2 + z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "-x",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 - y",
+ "-z",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 - x",
+ "-y"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/2 + x",
+ "1\/2 - y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "y",
+ "1\/2 - z",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "x",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 + y",
+ "z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 + x",
+ "y"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + z",
+ "x"
+ ],
+ [
+ "z",
+ "1\/2 - x",
+ "1\/2 + y"
+ ]
+ ]
+ },
+ "206":{
+ "SPGSym":"Ia-3",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "1\/2 - y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/2 - x",
+ "y"
+ ],
+ [
+ "-y",
+ "1\/2 - z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "1\/2 - y"
+ ],
+ [
+ "y",
+ "-z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "x",
+ "-y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "1\/2 + y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "1\/2 + x",
+ "-y"
+ ],
+ [
+ "y",
+ "1\/2 + z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "1\/2 + y"
+ ],
+ [
+ "-y",
+ "z",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "-x",
+ "y"
+ ]
+ ]
+ },
+ "207":{
+ "SPGSym":"P432",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "x",
+ "-z",
+ "y"
+ ],
+ [
+ "x",
+ "z",
+ "-y"
+ ],
+ [
+ "z",
+ "y",
+ "-x"
+ ],
+ [
+ "-z",
+ "y",
+ "x"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "z",
+ "-y",
+ "x"
+ ],
+ [
+ "-z",
+ "-y",
+ "-x"
+ ],
+ [
+ "-x",
+ "z",
+ "y"
+ ],
+ [
+ "-x",
+ "-z",
+ "-y"
+ ]
+ ]
+ },
+ "208":{
+ "SPGSym":"P4_232",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - z",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + z",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 + y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 + y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 - y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 - y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + z",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - z",
+ "1\/2 - y"
+ ]
+ ]
+ },
+ "209":{
+ "SPGSym":"F432",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "x",
+ "-z",
+ "y"
+ ],
+ [
+ "x",
+ "z",
+ "-y"
+ ],
+ [
+ "z",
+ "y",
+ "-x"
+ ],
+ [
+ "-z",
+ "y",
+ "x"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "z",
+ "-y",
+ "x"
+ ],
+ [
+ "-z",
+ "-y",
+ "-x"
+ ],
+ [
+ "-x",
+ "z",
+ "y"
+ ],
+ [
+ "-x",
+ "-z",
+ "-y"
+ ]
+ ]
+ },
+ "210":{
+ "SPGSym":"F4_132",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 - z",
+ "1\/4 + y"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 + z",
+ "1\/4 - y"
+ ],
+ [
+ "1\/4 + z",
+ "1\/4 + y",
+ "1\/4 - x"
+ ],
+ [
+ "1\/4 - z",
+ "1\/4 + y",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 + x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 - x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 + x",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 - x",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 + z",
+ "1\/4 - y",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 - z",
+ "1\/4 - y",
+ "1\/4 - x"
+ ],
+ [
+ "1\/4 - x",
+ "1\/4 + z",
+ "1\/4 + y"
+ ],
+ [
+ "1\/4 - x",
+ "1\/4 - z",
+ "1\/4 - y"
+ ]
+ ]
+ },
+ "211":{
+ "SPGSym":"I432",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "x",
+ "-z",
+ "y"
+ ],
+ [
+ "x",
+ "z",
+ "-y"
+ ],
+ [
+ "z",
+ "y",
+ "-x"
+ ],
+ [
+ "-z",
+ "y",
+ "x"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "z",
+ "-y",
+ "x"
+ ],
+ [
+ "-z",
+ "-y",
+ "-x"
+ ],
+ [
+ "-x",
+ "z",
+ "y"
+ ],
+ [
+ "-x",
+ "-z",
+ "-y"
+ ]
+ ]
+ },
+ "212":{
+ "SPGSym":"P4_332",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "1\/2 + z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "-x",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 - y",
+ "-z",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 - x",
+ "-y"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/2 + x",
+ "1\/2 - y"
+ ],
+ [
+ "3\/4 + x",
+ "3\/4 - z",
+ "1\/4 + y"
+ ],
+ [
+ "1\/4 + x",
+ "3\/4 + z",
+ "3\/4 - y"
+ ],
+ [
+ "1\/4 + z",
+ "3\/4 + y",
+ "3\/4 - x"
+ ],
+ [
+ "3\/4 - z",
+ "1\/4 + y",
+ "3\/4 + x"
+ ],
+ [
+ "3\/4 - y",
+ "1\/4 + x",
+ "3\/4 + z"
+ ],
+ [
+ "3\/4 + y",
+ "3\/4 - x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "3\/4 + x",
+ "3\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 - x",
+ "1\/4 - z"
+ ],
+ [
+ "3\/4 + z",
+ "3\/4 - y",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 - z",
+ "1\/4 - y",
+ "1\/4 - x"
+ ],
+ [
+ "3\/4 - x",
+ "1\/4 + z",
+ "3\/4 + y"
+ ],
+ [
+ "1\/4 - x",
+ "1\/4 - z",
+ "1\/4 - y"
+ ]
+ ]
+ },
+ "213":{
+ "SPGSym":"P4_132",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "1\/2 + z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "-x",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 - y",
+ "-z",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 - x",
+ "-y"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/2 + x",
+ "1\/2 - y"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 - z",
+ "3\/4 + y"
+ ],
+ [
+ "3\/4 + x",
+ "1\/4 + z",
+ "1\/4 - y"
+ ],
+ [
+ "3\/4 + z",
+ "1\/4 + y",
+ "1\/4 - x"
+ ],
+ [
+ "1\/4 - z",
+ "3\/4 + y",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 - y",
+ "3\/4 + x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 - x",
+ "3\/4 + z"
+ ],
+ [
+ "3\/4 + y",
+ "1\/4 + x",
+ "1\/4 - z"
+ ],
+ [
+ "3\/4 - y",
+ "3\/4 - x",
+ "3\/4 - z"
+ ],
+ [
+ "1\/4 + z",
+ "1\/4 - y",
+ "3\/4 + x"
+ ],
+ [
+ "3\/4 - z",
+ "3\/4 - y",
+ "3\/4 - x"
+ ],
+ [
+ "1\/4 - x",
+ "3\/4 + z",
+ "1\/4 + y"
+ ],
+ [
+ "3\/4 - x",
+ "3\/4 - z",
+ "3\/4 - y"
+ ]
+ ]
+ },
+ "214":{
+ "SPGSym":"I4_132",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "1\/2 - y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/2 - x",
+ "y"
+ ],
+ [
+ "-y",
+ "1\/2 - z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "1\/2 - y"
+ ],
+ [
+ "y",
+ "-z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "x",
+ "-y"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 - z",
+ "3\/4 + y"
+ ],
+ [
+ "3\/4 + x",
+ "1\/4 + z",
+ "1\/4 - y"
+ ],
+ [
+ "3\/4 + z",
+ "1\/4 + y",
+ "1\/4 - x"
+ ],
+ [
+ "1\/4 - z",
+ "3\/4 + y",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 - y",
+ "3\/4 + x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 - x",
+ "3\/4 + z"
+ ],
+ [
+ "3\/4 + y",
+ "1\/4 + x",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 - x",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 + z",
+ "1\/4 - y",
+ "3\/4 + x"
+ ],
+ [
+ "1\/4 - z",
+ "1\/4 - y",
+ "1\/4 - x"
+ ],
+ [
+ "1\/4 - x",
+ "3\/4 + z",
+ "1\/4 + y"
+ ],
+ [
+ "1\/4 - x",
+ "1\/4 - z",
+ "1\/4 - y"
+ ]
+ ]
+ },
+ "215":{
+ "SPGSym":"P-43m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "-x",
+ "z",
+ "-y"
+ ],
+ [
+ "-x",
+ "-z",
+ "y"
+ ],
+ [
+ "-z",
+ "-y",
+ "x"
+ ],
+ [
+ "z",
+ "-y",
+ "-x"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ],
+ [
+ "-z",
+ "y",
+ "-x"
+ ],
+ [
+ "z",
+ "y",
+ "x"
+ ],
+ [
+ "x",
+ "-z",
+ "-y"
+ ],
+ [
+ "x",
+ "z",
+ "y"
+ ]
+ ]
+ },
+ "216":{
+ "SPGSym":"F-43m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "-x",
+ "z",
+ "-y"
+ ],
+ [
+ "-x",
+ "-z",
+ "y"
+ ],
+ [
+ "-z",
+ "-y",
+ "x"
+ ],
+ [
+ "z",
+ "-y",
+ "-x"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ],
+ [
+ "-z",
+ "y",
+ "-x"
+ ],
+ [
+ "z",
+ "y",
+ "x"
+ ],
+ [
+ "x",
+ "-z",
+ "-y"
+ ],
+ [
+ "x",
+ "z",
+ "y"
+ ]
+ ]
+ },
+ "217":{
+ "SPGSym":"I-43m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "-x",
+ "z",
+ "-y"
+ ],
+ [
+ "-x",
+ "-z",
+ "y"
+ ],
+ [
+ "-z",
+ "-y",
+ "x"
+ ],
+ [
+ "z",
+ "-y",
+ "-x"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ],
+ [
+ "-z",
+ "y",
+ "-x"
+ ],
+ [
+ "z",
+ "y",
+ "x"
+ ],
+ [
+ "x",
+ "-z",
+ "-y"
+ ],
+ [
+ "x",
+ "z",
+ "y"
+ ]
+ ]
+ },
+ "218":{
+ "SPGSym":"P-43n",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + z",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - z",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 - y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 - y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 + y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 + y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - z",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + z",
+ "1\/2 + y"
+ ]
+ ]
+ },
+ "219":{
+ "SPGSym":"F-43c",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + z",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - z",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 - y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 - y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 + y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 + y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - z",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + z",
+ "1\/2 + y"
+ ]
+ ]
+ },
+ "220":{
+ "SPGSym":"I-43d",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "1\/2 - y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/2 - x",
+ "y"
+ ],
+ [
+ "-y",
+ "1\/2 - z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "1\/2 - y"
+ ],
+ [
+ "y",
+ "-z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "x",
+ "-y"
+ ],
+ [
+ "1\/4 - x",
+ "1\/4 + z",
+ "3\/4 - y"
+ ],
+ [
+ "3\/4 - x",
+ "1\/4 - z",
+ "1\/4 + y"
+ ],
+ [
+ "3\/4 - z",
+ "1\/4 - y",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 + z",
+ "3\/4 - y",
+ "1\/4 - x"
+ ],
+ [
+ "1\/4 + y",
+ "3\/4 - x",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 + x",
+ "3\/4 - z"
+ ],
+ [
+ "3\/4 - y",
+ "1\/4 - x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 + x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 - z",
+ "1\/4 + y",
+ "3\/4 - x"
+ ],
+ [
+ "1\/4 + z",
+ "1\/4 + y",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 + x",
+ "3\/4 - z",
+ "1\/4 - y"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 + z",
+ "1\/4 + y"
+ ]
+ ]
+ },
+ "221":{
+ "SPGSym":"Pm-3m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "x",
+ "-z",
+ "y"
+ ],
+ [
+ "x",
+ "z",
+ "-y"
+ ],
+ [
+ "z",
+ "y",
+ "-x"
+ ],
+ [
+ "-z",
+ "y",
+ "x"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "z",
+ "-y",
+ "x"
+ ],
+ [
+ "-z",
+ "-y",
+ "-x"
+ ],
+ [
+ "-x",
+ "z",
+ "y"
+ ],
+ [
+ "-x",
+ "-z",
+ "-y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "x",
+ "-y"
+ ],
+ [
+ "y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "y"
+ ],
+ [
+ "-y",
+ "z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "y"
+ ],
+ [
+ "-x",
+ "z",
+ "-y"
+ ],
+ [
+ "-x",
+ "-z",
+ "y"
+ ],
+ [
+ "-z",
+ "-y",
+ "x"
+ ],
+ [
+ "z",
+ "-y",
+ "-x"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ],
+ [
+ "-z",
+ "y",
+ "-x"
+ ],
+ [
+ "z",
+ "y",
+ "x"
+ ],
+ [
+ "x",
+ "-z",
+ "-y"
+ ],
+ [
+ "x",
+ "z",
+ "y"
+ ]
+ ]
+ },
+ "222":{
+ "SPGSym":"Pn-3n",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "1\/2 - y",
+ "z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 - x",
+ "y"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - z",
+ "x"
+ ],
+ [
+ "z",
+ "1\/2 - x",
+ "1\/2 - y"
+ ],
+ [
+ "y",
+ "1\/2 - z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "x",
+ "1\/2 - y"
+ ],
+ [
+ "x",
+ "1\/2 - z",
+ "y"
+ ],
+ [
+ "x",
+ "z",
+ "1\/2 - y"
+ ],
+ [
+ "z",
+ "y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "y",
+ "x"
+ ],
+ [
+ "1\/2 - y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "z",
+ "1\/2 - y",
+ "x"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 - y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - x",
+ "z",
+ "y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - z",
+ "1\/2 - y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "1\/2 + y",
+ "-z",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 + x",
+ "-y"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/2 + x",
+ "1\/2 + y"
+ ],
+ [
+ "-y",
+ "1\/2 + z",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "-x",
+ "1\/2 + y"
+ ],
+ [
+ "-x",
+ "1\/2 + z",
+ "-y"
+ ],
+ [
+ "-x",
+ "-z",
+ "1\/2 + y"
+ ],
+ [
+ "-z",
+ "-y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "-y",
+ "-x"
+ ],
+ [
+ "1\/2 + y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "-z",
+ "1\/2 + y",
+ "-x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 + y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + x",
+ "-z",
+ "-y"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + z",
+ "1\/2 + y"
+ ]
+ ]
+ },
+ "223":{
+ "SPGSym":"Pm-3n",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - z",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + z",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 + y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 + y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 - y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 - y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + z",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - z",
+ "1\/2 - y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "x",
+ "-y"
+ ],
+ [
+ "y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "y"
+ ],
+ [
+ "-y",
+ "z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + z",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - z",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 - y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 - y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 + y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 + y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - z",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + z",
+ "1\/2 + y"
+ ]
+ ]
+ },
+ "224":{
+ "SPGSym":"Pn-3m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 - y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "1\/2 - y",
+ "z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 - x",
+ "y"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - z",
+ "x"
+ ],
+ [
+ "z",
+ "1\/2 - x",
+ "1\/2 - y"
+ ],
+ [
+ "y",
+ "1\/2 - z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "x",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 + x",
+ "-z",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + z",
+ "-y"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 + y",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/2 + y",
+ "1\/2 + x"
+ ],
+ [
+ "-y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "-x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "1\/2 + z",
+ "-y",
+ "1\/2 + x"
+ ],
+ [
+ "-z",
+ "-y",
+ "-x"
+ ],
+ [
+ "-x",
+ "1\/2 + z",
+ "1\/2 + y"
+ ],
+ [
+ "-x",
+ "-z",
+ "-y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 + y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "1\/2 + y",
+ "-z",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 + x",
+ "-y"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/2 + x",
+ "1\/2 + y"
+ ],
+ [
+ "-y",
+ "1\/2 + z",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "-x",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 - x",
+ "z",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - z",
+ "y"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 - y",
+ "x"
+ ],
+ [
+ "z",
+ "1\/2 - y",
+ "1\/2 - x"
+ ],
+ [
+ "y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ],
+ [
+ "1\/2 - z",
+ "y",
+ "1\/2 - x"
+ ],
+ [
+ "z",
+ "y",
+ "x"
+ ],
+ [
+ "x",
+ "1\/2 - z",
+ "1\/2 - y"
+ ],
+ [
+ "x",
+ "z",
+ "y"
+ ]
+ ]
+ },
+ "225":{
+ "SPGSym":"Fm-3m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "x",
+ "-z",
+ "y"
+ ],
+ [
+ "x",
+ "z",
+ "-y"
+ ],
+ [
+ "z",
+ "y",
+ "-x"
+ ],
+ [
+ "-z",
+ "y",
+ "x"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "z",
+ "-y",
+ "x"
+ ],
+ [
+ "-z",
+ "-y",
+ "-x"
+ ],
+ [
+ "-x",
+ "z",
+ "y"
+ ],
+ [
+ "-x",
+ "-z",
+ "-y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "x",
+ "-y"
+ ],
+ [
+ "y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "y"
+ ],
+ [
+ "-y",
+ "z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "y"
+ ],
+ [
+ "-x",
+ "z",
+ "-y"
+ ],
+ [
+ "-x",
+ "-z",
+ "y"
+ ],
+ [
+ "-z",
+ "-y",
+ "x"
+ ],
+ [
+ "z",
+ "-y",
+ "-x"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ],
+ [
+ "-z",
+ "y",
+ "-x"
+ ],
+ [
+ "z",
+ "y",
+ "x"
+ ],
+ [
+ "x",
+ "-z",
+ "-y"
+ ],
+ [
+ "x",
+ "z",
+ "y"
+ ]
+ ]
+ },
+ "226":{
+ "SPGSym":"Fm-3c",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - z",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + z",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 + y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 + y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 - y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 - y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + z",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - z",
+ "1\/2 - y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "x",
+ "-y"
+ ],
+ [
+ "y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "y"
+ ],
+ [
+ "-y",
+ "z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 + z",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - z",
+ "1\/2 + y"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 - y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 - y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 + x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 + y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 + y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 - z",
+ "1\/2 - y"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + z",
+ "1\/2 + y"
+ ]
+ ]
+ },
+ "227":{
+ "SPGSym":"Fd-3m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/4 - y",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - x",
+ "y",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - x",
+ "1\/4 - y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "1\/4 - y",
+ "z",
+ "1\/4 - x"
+ ],
+ [
+ "1\/4 - z",
+ "1\/4 - x",
+ "y"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 - z",
+ "x"
+ ],
+ [
+ "z",
+ "1\/4 - x",
+ "1\/4 - y"
+ ],
+ [
+ "y",
+ "1\/4 - z",
+ "1\/4 - x"
+ ],
+ [
+ "1\/4 - z",
+ "x",
+ "1\/4 - y"
+ ],
+ [
+ "1\/4 + x",
+ "-z",
+ "1\/4 + y"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 + z",
+ "-y"
+ ],
+ [
+ "1\/4 + z",
+ "1\/4 + y",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/4 + y",
+ "1\/4 + x"
+ ],
+ [
+ "-y",
+ "1\/4 + x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "-x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 + x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "1\/4 + z",
+ "-y",
+ "1\/4 + x"
+ ],
+ [
+ "-z",
+ "-y",
+ "-x"
+ ],
+ [
+ "-x",
+ "1\/4 + z",
+ "1\/4 + y"
+ ],
+ [
+ "-x",
+ "-z",
+ "-y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/4 + y",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + x",
+ "-y",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 + y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "1\/4 + y",
+ "-z",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 + z",
+ "1\/4 + x",
+ "-y"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 + z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/4 + x",
+ "1\/4 + y"
+ ],
+ [
+ "-y",
+ "1\/4 + z",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 + z",
+ "-x",
+ "1\/4 + y"
+ ],
+ [
+ "1\/4 - x",
+ "z",
+ "1\/4 - y"
+ ],
+ [
+ "1\/4 - x",
+ "1\/4 - z",
+ "y"
+ ],
+ [
+ "1\/4 - z",
+ "1\/4 - y",
+ "x"
+ ],
+ [
+ "z",
+ "1\/4 - y",
+ "1\/4 - x"
+ ],
+ [
+ "y",
+ "1\/4 - x",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "x",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 - x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ],
+ [
+ "1\/4 - z",
+ "y",
+ "1\/4 - x"
+ ],
+ [
+ "z",
+ "y",
+ "x"
+ ],
+ [
+ "x",
+ "1\/4 - z",
+ "1\/4 - y"
+ ],
+ [
+ "x",
+ "z",
+ "y"
+ ]
+ ]
+ },
+ "228":{
+ "SPGSym":"Fd-3c",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/4 - y",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - x",
+ "y",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - x",
+ "1\/4 - y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "1\/4 - y",
+ "z",
+ "1\/4 - x"
+ ],
+ [
+ "1\/4 - z",
+ "1\/4 - x",
+ "y"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 - z",
+ "x"
+ ],
+ [
+ "z",
+ "1\/4 - x",
+ "1\/4 - y"
+ ],
+ [
+ "y",
+ "1\/4 - z",
+ "1\/4 - x"
+ ],
+ [
+ "1\/4 - z",
+ "x",
+ "1\/4 - y"
+ ],
+ [
+ "1\/4 + x",
+ "1\/2 - z",
+ "1\/4 + y"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 + z",
+ "1\/2 - y"
+ ],
+ [
+ "1\/4 + z",
+ "1\/4 + y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "1\/4 + y",
+ "1\/4 + x"
+ ],
+ [
+ "1\/2 - y",
+ "1\/4 + x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "1\/2 - x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 + x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - y",
+ "1\/2 - x",
+ "1\/2 - z"
+ ],
+ [
+ "1\/4 + z",
+ "1\/2 - y",
+ "1\/4 + x"
+ ],
+ [
+ "1\/2 - z",
+ "1\/2 - y",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - x",
+ "1\/4 + z",
+ "1\/4 + y"
+ ],
+ [
+ "1\/2 - x",
+ "1\/2 - z",
+ "1\/2 - y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/4 + y",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + x",
+ "-y",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 + y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "1\/4 + y",
+ "-z",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 + z",
+ "1\/4 + x",
+ "-y"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 + z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/4 + x",
+ "1\/4 + y"
+ ],
+ [
+ "-y",
+ "1\/4 + z",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 + z",
+ "-x",
+ "1\/4 + y"
+ ],
+ [
+ "1\/4 - x",
+ "1\/2 + z",
+ "1\/4 - y"
+ ],
+ [
+ "1\/4 - x",
+ "1\/4 - z",
+ "1\/2 + y"
+ ],
+ [
+ "1\/4 - z",
+ "1\/4 - y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/4 - y",
+ "1\/4 - x"
+ ],
+ [
+ "1\/2 + y",
+ "1\/4 - x",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "1\/2 + x",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 - x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + y",
+ "1\/2 + x",
+ "1\/2 + z"
+ ],
+ [
+ "1\/4 - z",
+ "1\/2 + y",
+ "1\/4 - x"
+ ],
+ [
+ "1\/2 + z",
+ "1\/2 + y",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + x",
+ "1\/4 - z",
+ "1\/4 - y"
+ ],
+ [
+ "1\/2 + x",
+ "1\/2 + z",
+ "1\/2 + y"
+ ]
+ ]
+ },
+ "229":{
+ "SPGSym":"Im-3m",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "-y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "-y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "-x",
+ "y"
+ ],
+ [
+ "-y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "-y"
+ ],
+ [
+ "y",
+ "-z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "-y"
+ ],
+ [
+ "x",
+ "-z",
+ "y"
+ ],
+ [
+ "x",
+ "z",
+ "-y"
+ ],
+ [
+ "z",
+ "y",
+ "-x"
+ ],
+ [
+ "-z",
+ "y",
+ "x"
+ ],
+ [
+ "-y",
+ "x",
+ "z"
+ ],
+ [
+ "y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "-z"
+ ],
+ [
+ "z",
+ "-y",
+ "x"
+ ],
+ [
+ "-z",
+ "-y",
+ "-x"
+ ],
+ [
+ "-x",
+ "z",
+ "y"
+ ],
+ [
+ "-x",
+ "-z",
+ "-y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "x",
+ "-y"
+ ],
+ [
+ "y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "y"
+ ],
+ [
+ "-y",
+ "z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "y"
+ ],
+ [
+ "-x",
+ "z",
+ "-y"
+ ],
+ [
+ "-x",
+ "-z",
+ "y"
+ ],
+ [
+ "-z",
+ "-y",
+ "x"
+ ],
+ [
+ "z",
+ "-y",
+ "-x"
+ ],
+ [
+ "y",
+ "-x",
+ "-z"
+ ],
+ [
+ "-y",
+ "x",
+ "-z"
+ ],
+ [
+ "-y",
+ "-x",
+ "z"
+ ],
+ [
+ "y",
+ "x",
+ "z"
+ ],
+ [
+ "-z",
+ "y",
+ "-x"
+ ],
+ [
+ "z",
+ "y",
+ "x"
+ ],
+ [
+ "x",
+ "-z",
+ "-y"
+ ],
+ [
+ "x",
+ "z",
+ "y"
+ ]
+ ]
+ },
+ "230":{
+ "SPGSym":"Ia-3d",
+ "SPGOps":[
+ [
+ "x",
+ "y",
+ "z"
+ ],
+ [
+ "x",
+ "-y",
+ "1\/2 - z"
+ ],
+ [
+ "1\/2 - x",
+ "y",
+ "-z"
+ ],
+ [
+ "-x",
+ "1\/2 - y",
+ "z"
+ ],
+ [
+ "z",
+ "x",
+ "y"
+ ],
+ [
+ "y",
+ "z",
+ "x"
+ ],
+ [
+ "1\/2 - y",
+ "z",
+ "-x"
+ ],
+ [
+ "-z",
+ "1\/2 - x",
+ "y"
+ ],
+ [
+ "-y",
+ "1\/2 - z",
+ "x"
+ ],
+ [
+ "z",
+ "-x",
+ "1\/2 - y"
+ ],
+ [
+ "y",
+ "-z",
+ "1\/2 - x"
+ ],
+ [
+ "1\/2 - z",
+ "x",
+ "-y"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 - z",
+ "3\/4 + y"
+ ],
+ [
+ "3\/4 + x",
+ "1\/4 + z",
+ "1\/4 - y"
+ ],
+ [
+ "3\/4 + z",
+ "1\/4 + y",
+ "1\/4 - x"
+ ],
+ [
+ "1\/4 - z",
+ "3\/4 + y",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 - y",
+ "3\/4 + x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 - x",
+ "3\/4 + z"
+ ],
+ [
+ "3\/4 + y",
+ "1\/4 + x",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 - x",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 + z",
+ "1\/4 - y",
+ "3\/4 + x"
+ ],
+ [
+ "1\/4 - z",
+ "1\/4 - y",
+ "1\/4 - x"
+ ],
+ [
+ "1\/4 - x",
+ "3\/4 + z",
+ "1\/4 + y"
+ ],
+ [
+ "1\/4 - x",
+ "1\/4 - z",
+ "1\/4 - y"
+ ],
+ [
+ "-x",
+ "-y",
+ "-z"
+ ],
+ [
+ "-x",
+ "y",
+ "1\/2 + z"
+ ],
+ [
+ "1\/2 + x",
+ "-y",
+ "z"
+ ],
+ [
+ "x",
+ "1\/2 + y",
+ "-z"
+ ],
+ [
+ "-z",
+ "-x",
+ "-y"
+ ],
+ [
+ "-y",
+ "-z",
+ "-x"
+ ],
+ [
+ "1\/2 + y",
+ "-z",
+ "x"
+ ],
+ [
+ "z",
+ "1\/2 + x",
+ "-y"
+ ],
+ [
+ "y",
+ "1\/2 + z",
+ "-x"
+ ],
+ [
+ "-z",
+ "x",
+ "1\/2 + y"
+ ],
+ [
+ "-y",
+ "z",
+ "1\/2 + x"
+ ],
+ [
+ "1\/2 + z",
+ "-x",
+ "y"
+ ],
+ [
+ "1\/4 - x",
+ "1\/4 + z",
+ "3\/4 - y"
+ ],
+ [
+ "3\/4 - x",
+ "1\/4 - z",
+ "1\/4 + y"
+ ],
+ [
+ "3\/4 - z",
+ "1\/4 - y",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 + z",
+ "3\/4 - y",
+ "1\/4 - x"
+ ],
+ [
+ "1\/4 + y",
+ "3\/4 - x",
+ "1\/4 - z"
+ ],
+ [
+ "1\/4 - y",
+ "1\/4 + x",
+ "3\/4 - z"
+ ],
+ [
+ "3\/4 - y",
+ "1\/4 - x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 + y",
+ "1\/4 + x",
+ "1\/4 + z"
+ ],
+ [
+ "1\/4 - z",
+ "1\/4 + y",
+ "3\/4 - x"
+ ],
+ [
+ "1\/4 + z",
+ "1\/4 + y",
+ "1\/4 + x"
+ ],
+ [
+ "1\/4 + x",
+ "3\/4 - z",
+ "1\/4 - y"
+ ],
+ [
+ "1\/4 + x",
+ "1\/4 + z",
+ "1\/4 + y"
+ ]
+ ]
+ }
+}
\ No newline at end of file