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spg_database.cpp
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spg_database.cpp
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/* This file is part of brille.
Copyright © 2019,2020 Greg Tucker <greg.tucker@stfc.ac.uk>
brille is free software: you can redistribute it and/or modify it under the
terms of the GNU Affero General Public License as published by the Free
Software Foundation, either version 3 of the License, or (at your option)
any later version.
brille is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.
See the GNU Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with brille. If not, see <https://www.gnu.org/licenses/>. */
/* This file has evolved from spg_database.cpp distributed as part of spglib.
Changes have been made to introduce C++ style classes as well as other
modifications to suit the needs of brille.
spglib was licensed under the following BSD 3-clause license:
Copyright (C) 2010 Atsushi Togo
All rights reserved.
This file is part of spglib. https://github.com/atztogo/spglib
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in
the documentation and/or other materials provided with the
distribution.
* Neither the name of the phonopy project nor the names of its
contributors may be used to endorse or promote products derived
from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE. */
#include <stdlib.h>
#include <cstring>
#include "spg_database.hpp"
#include "hall_symbol.hpp"
using namespace brille;
/* Modifications from spglib original:
' CENTERING_ERROR' --> 'Bravais::_'
' PRIMITIVE' --> 'Bravais::P'
' A_FACE' --> 'Bravais::A'
' B_FACE' --> 'Bravais::B' (not present)
' C_FACE' --> 'Bravais::C'
' BODY' --> 'Bravais::I'
' FACE' --> 'Bravais::F'
' R_CENTER' --> 'Bravais::R'
' BASE' --> 'Bravais::X' (not present)
2019-05-28 G Tucker */
/* The ALL_SPACEGROUP Spacegroup array has been switched from fixed-length char
arrays to variable length const std::strings (once initialized) */
/* In Hall symbols (3rd column), the double-prime is an escaped double quote*/
static const Spacegroup ALL_SPACEGROUPS[] = {
{ 0, "" , "" , "" , "" , "" , "" , Bravais::_, 0, 0},
{ 1, "C1^1" , "P 1" , "P 1" , "P 1" , "P1" , "" , Bravais::P, 1, 1},
{ 2, "Ci^1" , "-P 1" , "P -1" , "P -1" , "P-1" , "" , Bravais::P, 2, 2},
{ 3, "C2^1" , "P 2y" , "P 2 = P 1 2 1" , "P 1 2 1" , "P2" , "b" , Bravais::P, 3, 3},
{ 3, "C2^1" , "P 2" , "P 2 = P 1 1 2" , "P 1 1 2" , "P2" , "c" , Bravais::P, 3, 4},
{ 3, "C2^1" , "P 2x" , "P 2 = P 2 1 1" , "P 2 1 1" , "P2" , "a" , Bravais::P, 3, 5},
{ 4, "C2^2" , "P 2yb" , "P 2_1 = P 1 2_1 1" , "P 1 2_1 1" , "P2_1" , "b" , Bravais::P, 3, 6},
{ 4, "C2^2" , "P 2c" , "P 2_1 = P 1 1 2_1" , "P 1 1 2_1" , "P2_1" , "c" , Bravais::P, 3, 7},
{ 4, "C2^2" , "P 2xa" , "P 2_1 = P 2_1 1 1" , "P 2_1 1 1" , "P2_1" , "a" , Bravais::P, 3, 8},
{ 5, "C2^3" , "C 2y" , "C 2 = C 1 2 1" , "C 1 2 1" , "C2" , "b1" , Bravais::C, 3, 9},
{ 5, "C2^3" , "A 2y" , "C 2 = A 1 2 1" , "A 1 2 1" , "C2" , "b2" , Bravais::A, 3, 10},
{ 5, "C2^3" , "I 2y" , "C 2 = I 1 2 1" , "I 1 2 1" , "C2" , "b3" , Bravais::I, 3, 11},
{ 5, "C2^3" , "A 2" , "C 2 = A 1 1 2" , "A 1 1 2" , "C2" , "c1" , Bravais::A, 3, 12},
{ 5, "C2^3" , "B 2" , "C 2 = B 1 1 2 = B 2" , "B 1 1 2" , "C2" , "c2" , Bravais::P, 3, 13},
{ 5, "C2^3" , "I 2" , "C 2 = I 1 1 2" , "I 1 1 2" , "C2" , "c3" , Bravais::I, 3, 14},
{ 5, "C2^3" , "B 2x" , "C 2 = B 2 1 1" , "B 2 1 1" , "C2" , "a1" , Bravais::P, 3, 15},
{ 5, "C2^3" , "C 2x" , "C 2 = C 2 1 1" , "C 2 1 1" , "C2" , "a2" , Bravais::C, 3, 16},
{ 5, "C2^3" , "I 2x" , "C 2 = I 2 1 1" , "I 2 1 1" , "C2" , "a3" , Bravais::I, 3, 17},
{ 6, "Cs^1" , "P -2y" , "P m = P 1 m 1" , "P 1 m 1" , "Pm" , "b" , Bravais::P, 4, 18},
{ 6, "Cs^1" , "P -2" , "P m = P 1 1 m" , "P 1 1 m" , "Pm" , "c" , Bravais::P, 4, 19},
{ 6, "Cs^1" , "P -2x" , "P m = P m 1 1" , "P m 1 1" , "Pm" , "a" , Bravais::P, 4, 20},
{ 7, "Cs^2" , "P -2yc" , "P c = P 1 c 1" , "P 1 c 1" , "Pc" , "b1" , Bravais::P, 4, 21},
{ 7, "Cs^2" , "P -2yac" , "P c = P 1 n 1" , "P 1 n 1" , "Pc" , "b2" , Bravais::P, 4, 22},
{ 7, "Cs^2" , "P -2ya" , "P c = P 1 a 1" , "P 1 a 1" , "Pc" , "b3" , Bravais::P, 4, 23},
{ 7, "Cs^2" , "P -2a" , "P c = P 1 1 a" , "P 1 1 a" , "Pc" , "c1" , Bravais::P, 4, 24},
{ 7, "Cs^2" , "P -2ab" , "P c = P 1 1 n" , "P 1 1 n" , "Pc" , "c2" , Bravais::P, 4, 25},
{ 7, "Cs^2" , "P -2b" , "P c = P 1 1 b = P b" , "P 1 1 b" , "Pc" , "c3" , Bravais::P, 4, 26},
{ 7, "Cs^2" , "P -2xb" , "P c = P b 1 1" , "P b 1 1" , "Pc" , "a1" , Bravais::P, 4, 27},
{ 7, "Cs^2" , "P -2xbc" , "P c = P n 1 1" , "P n 1 1" , "Pc" , "a2" , Bravais::P, 4, 28},
{ 7, "Cs^2" , "P -2xc" , "P c = P c 1 1" , "P c 1 1" , "Pc" , "a3" , Bravais::P, 4, 29},
{ 8, "Cs^3" , "C -2y" , "C m = C 1 m 1" , "C 1 m 1" , "Cm" , "b1" , Bravais::C, 4, 30},
{ 8, "Cs^3" , "A -2y" , "C m = A 1 m 1" , "A 1 m 1" , "Cm" , "b2" , Bravais::A, 4, 31},
{ 8, "Cs^3" , "I -2y" , "C m = I 1 m 1" , "I 1 m 1" , "Cm" , "b3" , Bravais::I, 4, 32},
{ 8, "Cs^3" , "A -2" , "C m = A 1 1 m" , "A 1 1 m" , "Cm" , "c1" , Bravais::A, 4, 33},
{ 8, "Cs^3" , "B -2" , "C m = B 1 1 m = B m" , "B 1 1 m" , "Cm" , "c2" , Bravais::P, 4, 34},
{ 8, "Cs^3" , "I -2" , "C m = I 1 1 m" , "I 1 1 m" , "Cm" , "c3" , Bravais::I, 4, 35},
{ 8, "Cs^3" , "B -2x" , "C m = B m 1 1" , "B m 1 1" , "Cm" , "a1" , Bravais::P, 4, 36},
{ 8, "Cs^3" , "C -2x" , "C m = C m 1 1" , "C m 1 1" , "Cm" , "a2" , Bravais::C, 4, 37},
{ 8, "Cs^3" , "I -2x" , "C m = I m 1 1" , "I m 1 1" , "Cm" , "a3" , Bravais::I, 4, 38},
{ 9, "Cs^4" , "C -2yc" , "C c = C 1 c 1" , "C 1 c 1" , "Cc" , "b1" , Bravais::C, 4, 39},
{ 9, "Cs^4" , "A -2yac" , "C c = A 1 n 1" , "A 1 n 1" , "Cc" , "b2" , Bravais::A, 4, 40},
{ 9, "Cs^4" , "I -2ya" , "C c = I 1 a 1" , "I 1 a 1" , "Cc" , "b3" , Bravais::I, 4, 41},
{ 9, "Cs^4" , "A -2ya" , "C c = A 1 a 1" , "A 1 a 1" , "Cc" , "-b1" , Bravais::A, 4, 42},
{ 9, "Cs^4" , "C -2ybc" , "C c = C 1 n 1" , "C 1 n 1" , "Cc" , "-b2" , Bravais::C, 4, 43},
{ 9, "Cs^4" , "I -2yc" , "C c = I 1 c 1" , "I 1 c 1" , "Cc" , "-b3" , Bravais::I, 4, 44},
{ 9, "Cs^4" , "A -2a" , "C c = A 1 1 a" , "A 1 1 a" , "Cc" , "c1" , Bravais::A, 4, 45},
{ 9, "Cs^4" , "B -2bc" , "C c = B 1 1 n" , "B 1 1 n" , "Cc" , "c2" , Bravais::P, 4, 46},
{ 9, "Cs^4" , "I -2b" , "C c = I 1 1 b" , "I 1 1 b" , "Cc" , "c3" , Bravais::I, 4, 47},
{ 9, "Cs^4" , "B -2b" , "C c = B 1 1 b = B b" , "B 1 1 b" , "Cc" , "-c1" , Bravais::P, 4, 48},
{ 9, "Cs^4" , "A -2ac" , "C c = A 1 1 n" , "A 1 1 n" , "Cc" , "-c2" , Bravais::A, 4, 49},
{ 9, "Cs^4" , "I -2a" , "C c = I 1 1 a" , "I 1 1 a" , "Cc" , "-c3" , Bravais::I, 4, 50},
{ 9, "Cs^4" , "B -2xb" , "C c = B b 1 1" , "B b 1 1" , "Cc" , "a1" , Bravais::P, 4, 51},
{ 9, "Cs^4" , "C -2xbc" , "C c = C n 1 1" , "C n 1 1" , "Cc" , "a2" , Bravais::C, 4, 52},
{ 9, "Cs^4" , "I -2xc" , "C c = I c 1 1" , "I c 1 1" , "Cc" , "a3" , Bravais::I, 4, 53},
{ 9, "Cs^4" , "C -2xc" , "C c = C c 1 1" , "C c 1 1" , "Cc" , "-a1" , Bravais::C, 4, 54},
{ 9, "Cs^4" , "B -2xbc" , "C c = B n 1 1" , "B n 1 1" , "Cc" , "-a2" , Bravais::P, 4, 55},
{ 9, "Cs^4" , "I -2xb" , "C c = I b 1 1" , "I b 1 1" , "Cc" , "-a3" , Bravais::I, 4, 56},
{ 10, "C2h^1" , "-P 2y" , "P 2/m = P 1 2/m 1" , "P 1 2/m 1" , "P2/m" , "b" , Bravais::P, 5, 57},
{ 10, "C2h^1" , "-P 2" , "P 2/m = P 1 1 2/m" , "P 1 1 2/m" , "P2/m" , "c" , Bravais::P, 5, 58},
{ 10, "C2h^1" , "-P 2x" , "P 2/m = P 2/m 1 1" , "P 2/m 1 1" , "P2/m" , "a" , Bravais::P, 5, 59},
{ 11, "C2h^2" , "-P 2yb" , "P 2_1/m = P 1 2_1/m 1" , "P 1 2_1/m 1" , "P2_1/m" , "b" , Bravais::P, 5, 60},
{ 11, "C2h^2" , "-P 2c" , "P 2_1/m = P 1 1 2_1/m" , "P 1 1 2_1/m" , "P2_1/m" , "c" , Bravais::P, 5, 61},
{ 11, "C2h^2" , "-P 2xa" , "P 2_1/m = P 2_1/m 1 1" , "P 2_1/m 1 1" , "P2_1/m" , "a" , Bravais::P, 5, 62},
{ 12, "C2h^3" , "-C 2y" , "C 2/m = C 1 2/m 1" , "C 1 2/m 1" , "C2/m" , "b1" , Bravais::C, 5, 63},
{ 12, "C2h^3" , "-A 2y" , "C 2/m = A 1 2/m 1" , "A 1 2/m 1" , "C2/m" , "b2" , Bravais::A, 5, 64},
{ 12, "C2h^3" , "-I 2y" , "C 2/m = I 1 2/m 1" , "I 1 2/m 1" , "C2/m" , "b3" , Bravais::I, 5, 65},
{ 12, "C2h^3" , "-A 2" , "C 2/m = A 1 1 2/m" , "A 1 1 2/m" , "C2/m" , "c1" , Bravais::A, 5, 66},
{ 12, "C2h^3" , "-B 2" , "C 2/m = B 1 1 2/m = B 2/m" , "B 1 1 2/m" , "C2/m" , "c2" , Bravais::P, 5, 67},
{ 12, "C2h^3" , "-I 2" , "C 2/m = I 1 1 2/m" , "I 1 1 2/m" , "C2/m" , "c3" , Bravais::I, 5, 68},
{ 12, "C2h^3" , "-B 2x" , "C 2/m = B 2/m 1 1" , "B 2/m 1 1" , "C2/m" , "a1" , Bravais::P, 5, 69},
{ 12, "C2h^3" , "-C 2x" , "C 2/m = C 2/m 1 1" , "C 2/m 1 1" , "C2/m" , "a2" , Bravais::C, 5, 70},
{ 12, "C2h^3" , "-I 2x" , "C 2/m = I 2/m 1 1" , "I 2/m 1 1" , "C2/m" , "a3" , Bravais::I, 5, 71},
{ 13, "C2h^4" , "-P 2yc" , "P 2/c = P 1 2/c 1" , "P 1 2/c 1" , "P2/c" , "b1" , Bravais::P, 5, 72},
{ 13, "C2h^4" , "-P 2yac" , "P 2/c = P 1 2/n 1" , "P 1 2/n 1" , "P2/c" , "b2" , Bravais::P, 5, 73},
{ 13, "C2h^4" , "-P 2ya" , "P 2/c = P 1 2/a 1" , "P 1 2/a 1" , "P2/c" , "b3" , Bravais::P, 5, 74},
{ 13, "C2h^4" , "-P 2a" , "P 2/c = P 1 1 2/a" , "P 1 1 2/a" , "P2/c" , "c1" , Bravais::P, 5, 75},
{ 13, "C2h^4" , "-P 2ab" , "P 2/c = P 1 1 2/n" , "P 1 1 2/n" , "P2/c" , "c2" , Bravais::P, 5, 76},
{ 13, "C2h^4" , "-P 2b" , "P 2/c = P 1 1 2/b = P 2/b" , "P 1 1 2/b" , "P2/c" , "c3" , Bravais::P, 5, 77},
{ 13, "C2h^4" , "-P 2xb" , "P 2/c = P 2/b 1 1" , "P 2/b 1 1" , "P2/c" , "a1" , Bravais::P, 5, 78},
{ 13, "C2h^4" , "-P 2xbc" , "P 2/c = P 2/n 1 1" , "P 2/n 1 1" , "P2/c" , "a2" , Bravais::P, 5, 79},
{ 13, "C2h^4" , "-P 2xc" , "P 2/c = P 2/c 1 1" , "P 2/c 1 1" , "P2/c" , "a3" , Bravais::P, 5, 80},
{ 14, "C2h^5" , "-P 2ybc" , "P 2_1/c = P 1 2_1/c 1" , "P 1 2_1/c 1" , "P2_1/c" , "b1" , Bravais::P, 5, 81},
{ 14, "C2h^5" , "-P 2yn" , "P 2_1/c = P 1 2_1/n 1" , "P 1 2_1/n 1" , "P2_1/c" , "b2" , Bravais::P, 5, 82},
{ 14, "C2h^5" , "-P 2yab" , "P 2_1/c = P 1 2_1/a 1" , "P 1 2_1/a 1" , "P2_1/c" , "b3" , Bravais::P, 5, 83},
{ 14, "C2h^5" , "-P 2ac" , "P 2_1/c = P 1 1 2_1/a" , "P 1 1 2_1/a" , "P2_1/c" , "c1" , Bravais::P, 5, 84},
{ 14, "C2h^5" , "-P 2n" , "P 2_1/c = P 1 1 2_1/n" , "P 1 1 2_1/n" , "P2_1/c" , "c2" , Bravais::P, 5, 85},
{ 14, "C2h^5" , "-P 2bc" , "P 2_1/c = P 1 1 2_1/b = P 2_1/b", "P 1 1 2_1/b" , "P2_1/c" , "c3" , Bravais::P, 5, 86},
{ 14, "C2h^5" , "-P 2xab" , "P 2_1/c = P 2_1/b 1 1" , "P 2_1/b 1 1" , "P2_1/c" , "a1" , Bravais::P, 5, 87},
{ 14, "C2h^5" , "-P 2xn" , "P 2_1/c = P 2_1/n 1 1" , "P 2_1/n 1 1" , "P2_1/c" , "a2" , Bravais::P, 5, 88},
{ 14, "C2h^5" , "-P 2xac" , "P 2_1/c = P 2_1/c 1 1" , "P 2_1/c 1 1" , "P2_1/c" , "a3" , Bravais::P, 5, 89},
{ 15, "C2h^6" , "-C 2yc" , "C 2/c = C 1 2/c 1" , "C 1 2/c 1" , "C2/c" , "b1" , Bravais::C, 5, 90},
{ 15, "C2h^6" , "-A 2yac" , "C 2/c = A 1 2/n 1" , "A 1 2/n 1" , "C2/c" , "b2" , Bravais::A, 5, 91},
{ 15, "C2h^6" , "-I 2ya" , "C 2/c = I 1 2/a 1" , "I 1 2/a 1" , "C2/c" , "b3" , Bravais::I, 5, 92},
{ 15, "C2h^6" , "-A 2ya" , "C 2/c = A 1 2/a 1" , "A 1 2/a 1" , "C2/c" , "-b1" , Bravais::A, 5, 93},
{ 15, "C2h^6" , "-C 2ybc" , "C 2/c = C 1 2/n 1" , "C 1 2/n 1" , "C2/c" , "-b2" , Bravais::C, 5, 94},
{ 15, "C2h^6" , "-I 2yc" , "C 2/c = I 1 2/c 1" , "I 1 2/c 1" , "C2/c" , "-b3" , Bravais::I, 5, 95},
{ 15, "C2h^6" , "-A 2a" , "C 2/c = A 1 1 2/a" , "A 1 1 2/a" , "C2/c" , "c1" , Bravais::A, 5, 96},
{ 15, "C2h^6" , "-B 2bc" , "C 2/c = B 1 1 2/n" , "B 1 1 2/n" , "C2/c" , "c2" , Bravais::P, 5, 97},
{ 15, "C2h^6" , "-I 2b" , "C 2/c = I 1 1 2/b" , "I 1 1 2/b" , "C2/c" , "c3" , Bravais::I, 5, 98},
{ 15, "C2h^6" , "-B 2b" , "C 2/c = B 1 1 2/b = B 2/b" , "B 1 1 2/b" , "C2/c" , "-c1" , Bravais::P, 5, 99},
{ 15, "C2h^6" , "-A 2ac" , "C 2/c = A 1 1 2/n" , "A 1 1 2/n" , "C2/c" , "-c2" , Bravais::A, 5, 100},
{ 15, "C2h^6" , "-I 2a" , "C 2/c = I 1 1 2/a" , "I 1 1 2/a" , "C2/c" , "-c3" , Bravais::I, 5, 101},
{ 15, "C2h^6" , "-B 2xb" , "C 2/c = B 2/b 1 1" , "B 2/b 1 1" , "C2/c" , "a1" , Bravais::P, 5, 102},
{ 15, "C2h^6" , "-C 2xbc" , "C 2/c = C 2/n 1 1" , "C 2/n 1 1" , "C2/c" , "a2" , Bravais::C, 5, 103},
{ 15, "C2h^6" , "-I 2xc" , "C 2/c = I 2/c 1 1" , "I 2/c 1 1" , "C2/c" , "a3" , Bravais::I, 5, 104},
{ 15, "C2h^6" , "-C 2xc" , "C 2/c = C 2/c 1 1" , "C 2/c 1 1" , "C2/c" , "-a1" , Bravais::C, 5, 105},
{ 15, "C2h^6" , "-B 2xbc" , "C 2/c = B 2/n 1 1" , "B 2/n 1 1" , "C2/c" , "-a2" , Bravais::P, 5, 106},
{ 15, "C2h^6" , "-I 2xb" , "C 2/c = I 2/b 1 1" , "I 2/b 1 1" , "C2/c" , "-a3" , Bravais::I, 5, 107},
{ 16, "D2^1" , "P 2 2" , "P 2 2 2" , "P 2 2 2" , "P222" , "" , Bravais::P, 6, 108},
{ 17, "D2^2" , "P 2c 2" , "P 2 2 2_1" , "P 2 2 2_1" , "P222_1" , "" , Bravais::P, 6, 109},
{ 17, "D2^2" , "P 2a 2a" , "P 2_1 2 2" , "P 2_1 2 2" , "P2_122" , "cab" , Bravais::P, 6, 110},
{ 17, "D2^2" , "P 2 2b" , "P 2 2_1 2" , "P 2 2_1 2" , "P22_12" , "bca" , Bravais::P, 6, 111},
{ 18, "D2^3" , "P 2 2ab" , "P 2_1 2_1 2" , "P 2_1 2_1 2" , "P2_12_12" , "" , Bravais::P, 6, 112},
{ 18, "D2^3" , "P 2bc 2" , "P 2 2_1 2_1" , "P 2 2_1 2_1" , "P22_12_1" , "cab" , Bravais::P, 6, 113},
{ 18, "D2^3" , "P 2ac 2ac" , "P 2_1 2 2_1" , "P 2_1 2 2_1" , "P2_122_1" , "bca" , Bravais::P, 6, 114},
{ 19, "D2^4" , "P 2ac 2ab" , "P 2_1 2_1 2_1" , "P 2_1 2_1 2_1" , "P2_12_12_1", "" , Bravais::P, 6, 115},
{ 20, "D2^5" , "C 2c 2" , "C 2 2 2_1" , "C 2 2 2_1" , "C222_1" , "" , Bravais::C, 6, 116},
{ 20, "D2^5" , "A 2a 2a" , "A 2_1 2 2" , "A 2_1 2 2" , "A2_122" , "cab" , Bravais::A, 6, 117},
{ 20, "D2^5" , "B 2 2b" , "B 2 2_1 2" , "B 2 2_1 2" , "B22_12" , "bca" , Bravais::P, 6, 118},
{ 21, "D2^6" , "C 2 2" , "C 2 2 2" , "C 2 2 2" , "C222" , "" , Bravais::C, 6, 119},
{ 21, "D2^6" , "A 2 2" , "A 2 2 2" , "A 2 2 2" , "A222" , "cab" , Bravais::A, 6, 120},
{ 21, "D2^6" , "B 2 2" , "B 2 2 2" , "B 2 2 2" , "B222" , "bca" , Bravais::P, 6, 121},
{ 22, "D2^7" , "F 2 2" , "F 2 2 2" , "F 2 2 2" , "F222" , "" , Bravais::F, 6, 122},
{ 23, "D2^8" , "I 2 2" , "I 2 2 2" , "I 2 2 2" , "I222" , "" , Bravais::I, 6, 123},
{ 24, "D2^9" , "I 2b 2c" , "I 2_1 2_1 2_1" , "I 2_1 2_1 2_1" , "I2_12_12_1", "" , Bravais::I, 6, 124},
{ 25, "C2v^1" , "P 2 -2" , "P m m 2" , "P m m 2" , "Pmm2" , "" , Bravais::P, 7, 125},
{ 25, "C2v^1" , "P -2 2" , "P 2 m m" , "P 2 m m" , "P2mm" , "cab" , Bravais::P, 7, 126},
{ 25, "C2v^1" , "P -2 -2" , "P m 2 m" , "P m 2 m" , "Pm2m" , "bca" , Bravais::P, 7, 127},
{ 26, "C2v^2" , "P 2c -2" , "P m c 2_1" , "P m c 2_1" , "Pmc2_1" , "" , Bravais::P, 7, 128},
{ 26, "C2v^2" , "P 2c -2c" , "P c m 2_1" , "P c m 2_1" , "Pcm2_1" , "ba-c" , Bravais::P, 7, 129},
{ 26, "C2v^2" , "P -2a 2a" , "P 2_1 m a" , "P 2_1 m a" , "P2_1ma" , "cab" , Bravais::P, 7, 130},
{ 26, "C2v^2" , "P -2 2a" , "P 2_1 a m" , "P 2_1 a m" , "P2_1am" , "-cba" , Bravais::P, 7, 131},
{ 26, "C2v^2" , "P -2 -2b" , "P b 2_1 m" , "P b 2_1 m" , "Pb2_1m" , "bca" , Bravais::P, 7, 132},
{ 26, "C2v^2" , "P -2b -2" , "P m 2_1 b" , "P m 2_1 b" , "Pm2_1b" , "a-cb" , Bravais::P, 7, 133},
{ 27, "C2v^3" , "P 2 -2c" , "P c c 2" , "P c c 2" , "Pcc2" , "" , Bravais::P, 7, 134},
{ 27, "C2v^3" , "P -2a 2" , "P 2 a a" , "P 2 a a" , "P2aa" , "cab" , Bravais::P, 7, 135},
{ 27, "C2v^3" , "P -2b -2b" , "P b 2 b" , "P b 2 b" , "Pb2b" , "bca" , Bravais::P, 7, 136},
{ 28, "C2v^4" , "P 2 -2a" , "P m a 2" , "P m a 2" , "Pma2" , "" , Bravais::P, 7, 137},
{ 28, "C2v^4" , "P 2 -2b" , "P b m 2" , "P b m 2" , "Pbm2" , "ba-c" , Bravais::P, 7, 138},
{ 28, "C2v^4" , "P -2b 2" , "P 2 m b" , "P 2 m b" , "P2mb" , "cab" , Bravais::P, 7, 139},
{ 28, "C2v^4" , "P -2c 2" , "P 2 c m" , "P 2 c m" , "P2cm" , "-cba" , Bravais::P, 7, 140},
{ 28, "C2v^4" , "P -2c -2c" , "P c 2 m" , "P c 2 m" , "Pc2m" , "bca" , Bravais::P, 7, 141},
{ 28, "C2v^4" , "P -2a -2a" , "P m 2 a" , "P m 2 a" , "Pm2a" , "a-cb" , Bravais::P, 7, 142},
{ 29, "C2v^5" , "P 2c -2ac" , "P c a 2_1" , "P c a 2_1" , "Pca2_1" , "" , Bravais::P, 7, 143},
{ 29, "C2v^5" , "P 2c -2b" , "P b c 2_1" , "P b c 2_1" , "Pbc2_1" , "ba-c" , Bravais::P, 7, 144},
{ 29, "C2v^5" , "P -2b 2a" , "P 2_1 a b" , "P 2_1 a b" , "P2_1ab" , "cab" , Bravais::P, 7, 145},
{ 29, "C2v^5" , "P -2ac 2a" , "P 2_1 c a" , "P 2_1 c a" , "P2_1ca" , "-cba" , Bravais::P, 7, 146},
{ 29, "C2v^5" , "P -2bc -2c" , "P c 2_1 b" , "P c 2_1 b" , "Pc2_1b" , "bca" , Bravais::P, 7, 147},
{ 29, "C2v^5" , "P -2a -2ab" , "P b 2_1 a" , "P b 2_1 a" , "Pb2_1a" , "a-cb" , Bravais::P, 7, 148},
{ 30, "C2v^6" , "P 2 -2bc" , "P n c 2" , "P n c 2" , "Pnc2" , "" , Bravais::P, 7, 149},
{ 30, "C2v^6" , "P 2 -2ac" , "P c n 2" , "P c n 2" , "Pcn2" , "ba-c" , Bravais::P, 7, 150},
{ 30, "C2v^6" , "P -2ac 2" , "P 2 n a" , "P 2 n a" , "P2na" , "cab" , Bravais::P, 7, 151},
{ 30, "C2v^6" , "P -2ab 2" , "P 2 a n" , "P 2 a n" , "P2an" , "-cba" , Bravais::P, 7, 152},
{ 30, "C2v^6" , "P -2ab -2ab" , "P b 2 n" , "P b 2 n" , "Pb2n" , "bca" , Bravais::P, 7, 153},
{ 30, "C2v^6" , "P -2bc -2bc" , "P n 2 b" , "P n 2 b" , "Pn2b" , "a-cb" , Bravais::P, 7, 154},
{ 31, "C2v^7" , "P 2ac -2" , "P m n 2_1" , "P m n 2_1" , "Pmn2_1" , "" , Bravais::P, 7, 155},
{ 31, "C2v^7" , "P 2bc -2bc" , "P n m 2_1" , "P n m 2_1" , "Pnm2_1" , "ba-c" , Bravais::P, 7, 156},
{ 31, "C2v^7" , "P -2ab 2ab" , "P 2_1 m n" , "P 2_1 m n" , "P2_1mn" , "cab" , Bravais::P, 7, 157},
{ 31, "C2v^7" , "P -2 2ac" , "P 2_1 n m" , "P 2_1 n m" , "P2_1nm" , "-cba" , Bravais::P, 7, 158},
{ 31, "C2v^7" , "P -2 -2bc" , "P n 2_1 m" , "P n 2_1 m" , "Pn2_1m" , "bca" , Bravais::P, 7, 159},
{ 31, "C2v^7" , "P -2ab -2" , "P m 2_1 n" , "P m 2_1 n" , "Pm2_1n" , "a-cb" , Bravais::P, 7, 160},
{ 32, "C2v^8" , "P 2 -2ab" , "P b a 2" , "P b a 2" , "Pba2" , "" , Bravais::P, 7, 161},
{ 32, "C2v^8" , "P -2bc 2" , "P 2 c b" , "P 2 c b" , "P2cb" , "cab" , Bravais::P, 7, 162},
{ 32, "C2v^8" , "P -2ac -2ac" , "P c 2 a" , "P c 2 a" , "Pc2a" , "bca" , Bravais::P, 7, 163},
{ 33, "C2v^9" , "P 2c -2n" , "P n a 2_1" , "P n a 2_1" , "Pna2_1" , "" , Bravais::P, 7, 164},
{ 33, "C2v^9" , "P 2c -2ab" , "P b n 2_1" , "P b n 2_1" , "Pbn2_1" , "ba-c" , Bravais::P, 7, 165},
{ 33, "C2v^9" , "P -2bc 2a" , "P 2_1 n b" , "P 2_1 n b" , "P2_1nb" , "cab" , Bravais::P, 7, 166},
{ 33, "C2v^9" , "P -2n 2a" , "P 2_1 c n" , "P 2_1 c n" , "P2_1cn" , "-cba" , Bravais::P, 7, 167},
{ 33, "C2v^9" , "P -2n -2ac" , "P c 2_1 n" , "P c 2_1 n" , "Pc2_1n" , "bca" , Bravais::P, 7, 168},
{ 33, "C2v^9" , "P -2ac -2n" , "P n 2_1 a" , "P n 2_1 a" , "Pn2_1a" , "a-cb" , Bravais::P, 7, 169},
{ 34, "C2v^10", "P 2 -2n" , "P n n 2" , "P n n 2" , "Pnn2" , "" , Bravais::P, 7, 170},
{ 34, "C2v^10", "P -2n 2" , "P 2 n n" , "P 2 n n" , "P2nn" , "cab" , Bravais::P, 7, 171},
{ 34, "C2v^10", "P -2n -2n" , "P n 2 n" , "P n 2 n" , "Pn2n" , "bca" , Bravais::P, 7, 172},
{ 35, "C2v^11", "C 2 -2" , "C m m 2" , "C m m 2" , "Cmm2" , "" , Bravais::C, 7, 173},
{ 35, "C2v^11", "A -2 2" , "A 2 m m" , "A 2 m m" , "A2mm" , "cab" , Bravais::A, 7, 174},
{ 35, "C2v^11", "B -2 -2" , "B m 2 m" , "B m 2 m" , "Bm2m" , "bca" , Bravais::P, 7, 175},
{ 36, "C2v^12", "C 2c -2" , "C m c 2_1" , "C m c 2_1" , "Cmc2_1" , "" , Bravais::C, 7, 176},
{ 36, "C2v^12", "C 2c -2c" , "C c m 2_1" , "C c m 2_1" , "Ccm2_1" , "ba-c" , Bravais::C, 7, 177},
{ 36, "C2v^12", "A -2a 2a" , "A 2_1 m a" , "A 2_1 m a" , "A2_1ma" , "cab" , Bravais::A, 7, 178},
{ 36, "C2v^12", "A -2 2a" , "A 2_1 a m" , "A 2_1 a m" , "A2_1am" , "-cba" , Bravais::A, 7, 179},
{ 36, "C2v^12", "B -2 -2b" , "B b 2_1 m" , "B b 2_1 m" , "Bb2_1m" , "bca" , Bravais::P, 7, 180},
{ 36, "C2v^12", "B -2b -2" , "B m 2_1 b" , "B m 2_1 b" , "Bm2_1b" , "a-cb" , Bravais::P, 7, 181},
{ 37, "C2v^13", "C 2 -2c" , "C c c 2" , "C c c 2" , "Ccc2" , "" , Bravais::C, 7, 182},
{ 37, "C2v^13", "A -2a 2" , "A 2 a a" , "A 2 a a" , "A2aa" , "cab" , Bravais::A, 7, 183},
{ 37, "C2v^13", "B -2b -2b" , "B b 2 b" , "B b 2 b" , "Bb2b" , "bca" , Bravais::P, 7, 184},
{ 38, "C2v^14", "A 2 -2" , "A m m 2" , "A m m 2" , "Amm2" , "" , Bravais::A, 7, 185},
{ 38, "C2v^14", "B 2 -2" , "B m m 2" , "B m m 2" , "Bmm2" , "ba-c" , Bravais::P, 7, 186},
{ 38, "C2v^14", "B -2 2" , "B 2 m m" , "B 2 m m" , "B2mm" , "cab" , Bravais::P, 7, 187},
{ 38, "C2v^14", "C -2 2" , "C 2 m m" , "C 2 m m" , "C2mm" , "-cba" , Bravais::C, 7, 188},
{ 38, "C2v^14", "C -2 -2" , "C m 2 m" , "C m 2 m" , "Cm2m" , "bca" , Bravais::C, 7, 189},
{ 38, "C2v^14", "A -2 -2" , "A m 2 m" , "A m 2 m" , "Am2m" , "a-cb" , Bravais::A, 7, 190},
{ 39, "C2v^15", "A 2 -2c" , "A e m 2" , "A e m 2" , "Aem2" , "" , Bravais::A, 7, 191},
{ 39, "C2v^15", "B 2 -2c" , "B m e 2" , "B m e 2" , "Bme2" , "ba-c" , Bravais::P, 7, 192},
{ 39, "C2v^15", "B -2c 2" , "B 2 e m" , "B 2 e m" , "B2em" , "cab" , Bravais::P, 7, 193},
{ 39, "C2v^15", "C -2b 2" , "C 2 m e" , "C 2 m e" , "C2me" , "-cba" , Bravais::C, 7, 194},
{ 39, "C2v^15", "C -2b -2b" , "C m 2 e" , "C m 2 e" , "Cm2e" , "bca" , Bravais::C, 7, 195},
{ 39, "C2v^15", "A -2c -2c" , "A e 2 m" , "A e 2 m" , "Ae2m" , "a-cb" , Bravais::A, 7, 196},
{ 40, "C2v^16", "A 2 -2a" , "A m a 2" , "A m a 2" , "Ama2" , "" , Bravais::A, 7, 197},
{ 40, "C2v^16", "B 2 -2b" , "B b m 2" , "B b m 2" , "Bbm2" , "ba-c" , Bravais::P, 7, 198},
{ 40, "C2v^16", "B -2b 2" , "B 2 m b" , "B 2 m b" , "B2mb" , "cab" , Bravais::P, 7, 199},
{ 40, "C2v^16", "C -2c 2" , "C 2 c m" , "C 2 c m" , "C2cm" , "-cba" , Bravais::C, 7, 200},
{ 40, "C2v^16", "C -2c -2c" , "C c 2 m" , "C c 2 m" , "Cc2m" , "bca" , Bravais::C, 7, 201},
{ 40, "C2v^16", "A -2a -2a" , "A m 2 a" , "A m 2 a" , "Am2a" , "a-cb" , Bravais::A, 7, 202},
{ 41, "C2v^17", "A 2 -2ac" , "A e a 2" , "A e a 2" , "Aea2" , "" , Bravais::A, 7, 203},
{ 41, "C2v^17", "B 2 -2bc" , "B b e 2" , "B b e 2" , "Bbe2" , "ba-c" , Bravais::P, 7, 204},
{ 41, "C2v^17", "B -2bc 2" , "B 2 e b" , "B 2 e b" , "B2eb" , "cab" , Bravais::P, 7, 205},
{ 41, "C2v^17", "C -2bc 2" , "C 2 c e" , "C 2 c e" , "C2ce" , "-cba" , Bravais::C, 7, 206},
{ 41, "C2v^17", "C -2bc -2bc" , "C c 2 e" , "C c 2 e" , "Cc2e" , "bca" , Bravais::C, 7, 207},
{ 41, "C2v^17", "A -2ac -2ac" , "A e 2 a" , "A e 2 a" , "Ae2a" , "a-cb" , Bravais::A, 7, 208},
{ 42, "C2v^18", "F 2 -2" , "F m m 2" , "F m m 2" , "Fmm2" , "" , Bravais::F, 7, 209},
{ 42, "C2v^18", "F -2 2" , "F 2 m m" , "F 2 m m" , "F2mm" , "cab" , Bravais::F, 7, 210},
{ 42, "C2v^18", "F -2 -2" , "F m 2 m" , "F m 2 m" , "Fm2m" , "bca" , Bravais::F, 7, 211},
{ 43, "C2v^19", "F 2 -2d" , "F d d 2" , "F d d 2" , "Fdd2" , "" , Bravais::F, 7, 212},
{ 43, "C2v^19", "F -2d 2" , "F 2 d d" , "F 2 d d" , "F2dd" , "cab" , Bravais::F, 7, 213},
{ 43, "C2v^19", "F -2d -2d" , "F d 2 d" , "F d 2 d" , "Fd2d" , "bca" , Bravais::F, 7, 214},
{ 44, "C2v^20", "I 2 -2" , "I m m 2" , "I m m 2" , "Imm2" , "" , Bravais::I, 7, 215},
{ 44, "C2v^20", "I -2 2" , "I 2 m m" , "I 2 m m" , "I2mm" , "cab" , Bravais::I, 7, 216},
{ 44, "C2v^20", "I -2 -2" , "I m 2 m" , "I m 2 m" , "Im2m" , "bca" , Bravais::I, 7, 217},
{ 45, "C2v^21", "I 2 -2c" , "I b a 2" , "I b a 2" , "Iba2" , "" , Bravais::I, 7, 218},
{ 45, "C2v^21", "I -2a 2" , "I 2 c b" , "I 2 c b" , "I2cb" , "cab" , Bravais::I, 7, 219},
{ 45, "C2v^21", "I -2b -2b" , "I c 2 a" , "I c 2 a" , "Ic2a" , "bca" , Bravais::I, 7, 220},
{ 46, "C2v^22", "I 2 -2a" , "I m a 2" , "I m a 2" , "Ima2" , "" , Bravais::I, 7, 221},
{ 46, "C2v^22", "I 2 -2b" , "I b m 2" , "I b m 2" , "Ibm2" , "ba-c" , Bravais::I, 7, 222},
{ 46, "C2v^22", "I -2b 2" , "I 2 m b" , "I 2 m b" , "I2mb" , "cab" , Bravais::I, 7, 223},
{ 46, "C2v^22", "I -2c 2" , "I 2 c m" , "I 2 c m" , "I2cm" , "-cba" , Bravais::I, 7, 224},
{ 46, "C2v^22", "I -2c -2c" , "I c 2 m" , "I c 2 m" , "Ic2m" , "bca" , Bravais::I, 7, 225},
{ 46, "C2v^22", "I -2a -2a" , "I m 2 a" , "I m 2 a" , "Im2a" , "a-cb" , Bravais::I, 7, 226},
{ 47, "D2h^1" , "-P 2 2" , "P m m m" , "P 2/m 2/m 2/m" , "Pmmm" , "" , Bravais::P, 8, 227},
{ 48, "D2h^2" , "P 2 2 -1n" , "P n n n" , "P 2/n 2/n 2/n" , "Pnnn" , "1" , Bravais::P, 8, 228},
{ 48, "D2h^2" , "-P 2ab 2bc" , "P n n n" , "P 2/n 2/n 2/n" , "Pnnn" , "2" , Bravais::P, 8, 229},
{ 49, "D2h^3" , "-P 2 2c" , "P c c m" , "P 2/c 2/c 2/m" , "Pccm" , "" , Bravais::P, 8, 230},
{ 49, "D2h^3" , "-P 2a 2" , "P m a a" , "P 2/m 2/a 2/a" , "Pmaa" , "cab" , Bravais::P, 8, 231},
{ 49, "D2h^3" , "-P 2b 2b" , "P b m b" , "P 2/b 2/m 2/b" , "Pbmb" , "bca" , Bravais::P, 8, 232},
{ 50, "D2h^4" , "P 2 2 -1ab" , "P b a n" , "P 2/b 2/a 2/n" , "Pban" , "1" , Bravais::P, 8, 233},
{ 50, "D2h^4" , "-P 2ab 2b" , "P b a n" , "P 2/b 2/a 2/n" , "Pban" , "2" , Bravais::P, 8, 234},
{ 50, "D2h^4" , "P 2 2 -1bc" , "P n c b" , "P 2/n 2/c 2/b" , "Pncb" , "1cab" , Bravais::P, 8, 235},
{ 50, "D2h^4" , "-P 2b 2bc" , "P n c b" , "P 2/n 2/c 2/b" , "Pncb" , "2cab" , Bravais::P, 8, 236},
{ 50, "D2h^4" , "P 2 2 -1ac" , "P c n a" , "P 2/c 2/n 2/a" , "Pcna" , "1bca" , Bravais::P, 8, 237},
{ 50, "D2h^4" , "-P 2a 2c" , "P c n a" , "P 2/c 2/n 2/a" , "Pcna" , "2bca" , Bravais::P, 8, 238},
{ 51, "D2h^5" , "-P 2a 2a" , "P m m a" , "P 2_1/m 2/m 2/a" , "Pmma" , "" , Bravais::P, 8, 239},
{ 51, "D2h^5" , "-P 2b 2" , "P m m b" , "P 2/m 2_1/m 2/b" , "Pmmb" , "ba-c" , Bravais::P, 8, 240},
{ 51, "D2h^5" , "-P 2 2b" , "P b m m" , "P 2/b 2_1/m 2/m" , "Pbmm" , "cab" , Bravais::P, 8, 241},
{ 51, "D2h^5" , "-P 2c 2c" , "P c m m" , "P 2/c 2/m 2_1/m" , "Pcmm" , "-cba" , Bravais::P, 8, 242},
{ 51, "D2h^5" , "-P 2c 2" , "P m c m" , "P 2/m 2/c 2_1/m" , "Pmcm" , "bca" , Bravais::P, 8, 243},
{ 51, "D2h^5" , "-P 2 2a" , "P m a m" , "P 2_1/m 2/a 2/m" , "Pmam" , "a-cb" , Bravais::P, 8, 244},
{ 52, "D2h^6" , "-P 2a 2bc" , "P n n a" , "P 2/n 2_1/n 2/a" , "Pnna" , "" , Bravais::P, 8, 245},
{ 52, "D2h^6" , "-P 2b 2n" , "P n n b" , "P 2_1/n 2/n 2/b" , "Pnnb" , "ba-c" , Bravais::P, 8, 246},
{ 52, "D2h^6" , "-P 2n 2b" , "P b n n" , "P 2/b 2/n 2_1/n" , "Pbnn" , "cab" , Bravais::P, 8, 247},
{ 52, "D2h^6" , "-P 2ab 2c" , "P c n n" , "P 2/c 2_1/n 2/n" , "Pcnn" , "-cba" , Bravais::P, 8, 248},
{ 52, "D2h^6" , "-P 2ab 2n" , "P n c n" , "P 2_1/n 2/c 2/n" , "Pncn" , "bca" , Bravais::P, 8, 249},
{ 52, "D2h^6" , "-P 2n 2bc" , "P n a n" , "P 2/n 2/a 2_1/n" , "Pnan" , "a-cb" , Bravais::P, 8, 250},
{ 53, "D2h^7" , "-P 2ac 2" , "P m n a" , "P 2/m 2/n 2_1/a" , "Pmna" , "" , Bravais::P, 8, 251},
{ 53, "D2h^7" , "-P 2bc 2bc" , "P n m b" , "P 2/n 2/m 2_1/b" , "Pnmb" , "ba-c" , Bravais::P, 8, 252},
{ 53, "D2h^7" , "-P 2ab 2ab" , "P b m n" , "P 2_1/b 2/m 2/n" , "Pbmn" , "cab" , Bravais::P, 8, 253},
{ 53, "D2h^7" , "-P 2 2ac" , "P c n m" , "P 2_1/c 2/n 2/m" , "Pcnm" , "-cba" , Bravais::P, 8, 254},
{ 53, "D2h^7" , "-P 2 2bc" , "P n c m" , "P 2/n 2_1/c 2/m" , "Pncm" , "bca" , Bravais::P, 8, 255},
{ 53, "D2h^7" , "-P 2ab 2" , "P m a n" , "P 2/m 2_1/a 2/n" , "Pman" , "a-cb" , Bravais::P, 8, 256},
{ 54, "D2h^8" , "-P 2a 2ac" , "P c c a" , "P 2_1/c 2/c 2/a" , "Pcca" , "" , Bravais::P, 8, 257},
{ 54, "D2h^8" , "-P 2b 2c" , "P c c b" , "P 2/c 2_1/c 2/b" , "Pccb" , "ba-c" , Bravais::P, 8, 258},
{ 54, "D2h^8" , "-P 2a 2b" , "P b a a" , "P 2/b 2_1/a 2/a" , "Pbaa" , "cab" , Bravais::P, 8, 259},
{ 54, "D2h^8" , "-P 2ac 2c" , "P c a a" , "P 2/c 2/a 2_1/a" , "Pcaa" , "-cba" , Bravais::P, 8, 260},
{ 54, "D2h^8" , "-P 2bc 2b" , "P b c b" , "P 2/b 2/c 2_1/b" , "Pbcb" , "bca" , Bravais::P, 8, 261},
{ 54, "D2h^8" , "-P 2b 2ab" , "P b a b" , "P 2_1/b 2/a 2/b" , "Pbab" , "a-cb" , Bravais::P, 8, 262},
{ 55, "D2h^9" , "-P 2 2ab" , "P b a m" , "P 2_1/b 2_1/a 2/m" , "Pbam" , "" , Bravais::P, 8, 263},
{ 55, "D2h^9" , "-P 2bc 2" , "P m c b" , "P 2/m 2_1/c 2_1/b" , "Pmcb" , "cab" , Bravais::P, 8, 264},
{ 55, "D2h^9" , "-P 2ac 2ac" , "P c m a" , "P 2_1/c 2/m 2_1/a" , "Pcma" , "bca" , Bravais::P, 8, 265},
{ 56, "D2h^10", "-P 2ab 2ac" , "P c c n" , "P 2_1/c 2_1/c 2/n" , "Pccn" , "" , Bravais::P, 8, 266},
{ 56, "D2h^10", "-P 2ac 2bc" , "P n a a" , "P 2/n 2_1/a 2_1/a" , "Pnaa" , "cab" , Bravais::P, 8, 267},
{ 56, "D2h^10", "-P 2bc 2ab" , "P b n b" , "P 2_1/b 2/n 2_1/b" , "Pbnb" , "bca" , Bravais::P, 8, 268},
{ 57, "D2h^11", "-P 2c 2b" , "P b c m" , "P 2/b 2_1/c 2_1/m" , "Pbcm" , "" , Bravais::P, 8, 269},
{ 57, "D2h^11", "-P 2c 2ac" , "P c a m" , "P 2_1/c 2/a 2_1/m" , "Pcam" , "ba-c" , Bravais::P, 8, 270},
{ 57, "D2h^11", "-P 2ac 2a" , "P m c a" , "P 2_1/m 2/c 2_1/a" , "Pmca" , "cab" , Bravais::P, 8, 271},
{ 57, "D2h^11", "-P 2b 2a" , "P m a b" , "P 2_1/m 2_1/a 2/b" , "Pmab" , "-cba" , Bravais::P, 8, 272},
{ 57, "D2h^11", "-P 2a 2ab" , "P b m a" , "P 2_1/b 2_1/m 2/a" , "Pbma" , "bca" , Bravais::P, 8, 273},
{ 57, "D2h^11", "-P 2bc 2c" , "P c m b" , "P 2/c 2_1/m 2_1/b" , "Pcmb" , "a-cb" , Bravais::P, 8, 274},
{ 58, "D2h^12", "-P 2 2n" , "P n n m" , "P 2_1/n 2_1/n 2/m" , "Pnnm" , "" , Bravais::P, 8, 275},
{ 58, "D2h^12", "-P 2n 2" , "P m n n" , "P 2/m 2_1/n 2_1/n" , "Pmnn" , "cab" , Bravais::P, 8, 276},
{ 58, "D2h^12", "-P 2n 2n" , "P n m n" , "P 2_1/n 2/m 2_1/n" , "Pnmn" , "bca" , Bravais::P, 8, 277},
{ 59, "D2h^13", "P 2 2ab -1ab" , "P m m n" , "P 2_1/m 2_1/m 2/n" , "Pmmn" , "1" , Bravais::P, 8, 278},
{ 59, "D2h^13", "-P 2ab 2a" , "P m m n" , "P 2_1/m 2_1/m 2/n" , "Pmmn" , "2" , Bravais::P, 8, 279},
{ 59, "D2h^13", "P 2bc 2 -1bc" , "P n m m" , "P 2/n 2_1/m 2_1/m" , "Pnmm" , "1cab" , Bravais::P, 8, 280},
{ 59, "D2h^13", "-P 2c 2bc" , "P n m m" , "P 2/n 2_1/m 2_1/m" , "Pnmm" , "2cab" , Bravais::P, 8, 281},
{ 59, "D2h^13", "P 2ac 2ac -1ac" , "P m n m" , "P 2_1/m 2/n 2_1/m" , "Pmnm" , "1bca" , Bravais::P, 8, 282},
{ 59, "D2h^13", "-P 2c 2a" , "P m n m" , "P 2_1/m 2/n 2_1/m" , "Pmnm" , "2bca" , Bravais::P, 8, 283},
{ 60, "D2h^14", "-P 2n 2ab" , "P b c n" , "P 2_1/b 2/c 2_1/n" , "Pbcn" , "" , Bravais::P, 8, 284},
{ 60, "D2h^14", "-P 2n 2c" , "P c a n" , "P 2/c 2_1/a 2_1/n" , "Pcan" , "ba-c" , Bravais::P, 8, 285},
{ 60, "D2h^14", "-P 2a 2n" , "P n c a" , "P 2_1/n 2_1/c 2/a" , "Pnca" , "cab" , Bravais::P, 8, 286},
{ 60, "D2h^14", "-P 2bc 2n" , "P n a b" , "P 2_1/n 2/a 2_1/b" , "Pnab" , "-cba" , Bravais::P, 8, 287},
{ 60, "D2h^14", "-P 2ac 2b" , "P b n a" , "P 2/b 2_1/n 2_1/a" , "Pbna" , "bca" , Bravais::P, 8, 288},
{ 60, "D2h^14", "-P 2b 2ac" , "P c n b" , "P 2_1/c 2_1/n 2/b" , "Pcnb" , "a-cb" , Bravais::P, 8, 289},
{ 61, "D2h^15", "-P 2ac 2ab" , "P b c a" , "P 2_1/b 2_1/c 2_1/a", "Pbca" , "" , Bravais::P, 8, 290},
{ 61, "D2h^15", "-P 2bc 2ac" , "P c a b" , "P 2_1/c 2_1/a 2_1/b", "Pcab" , "ba-c" , Bravais::P, 8, 291},
{ 62, "D2h^16", "-P 2ac 2n" , "P n m a" , "P 2_1/n 2_1/m 2_1/a", "Pnma" , "" , Bravais::P, 8, 292},
{ 62, "D2h^16", "-P 2bc 2a" , "P m n b" , "P 2_1/m 2_1/n 2_1/b", "Pmnb" , "ba-c" , Bravais::P, 8, 293},
{ 62, "D2h^16", "-P 2c 2ab" , "P b n m" , "P 2_1/b 2_1/n 2_1/m", "Pbnm" , "cab" , Bravais::P, 8, 294},
{ 62, "D2h^16", "-P 2n 2ac" , "P c m n" , "P 2_1/c 2_1/m 2_1/n", "Pcmn" , "-cba" , Bravais::P, 8, 295},
{ 62, "D2h^16", "-P 2n 2a" , "P m c n" , "P 2_1/m 2_1/c 2_1/n", "Pmcn" , "bca" , Bravais::P, 8, 296},
{ 62, "D2h^16", "-P 2c 2n" , "P n a m" , "P 2_1/n 2_1/a 2_1/m", "Pnam" , "a-cb" , Bravais::P, 8, 297},
{ 63, "D2h^17", "-C 2c 2" , "C m c m" , "C 2/m 2/c 2_1/m" , "Cmcm" , "" , Bravais::C, 8, 298},
{ 63, "D2h^17", "-C 2c 2c" , "C c m m" , "C 2/c 2/m 2_1/m" , "Ccmm" , "ba-c" , Bravais::C, 8, 299},
{ 63, "D2h^17", "-A 2a 2a" , "A m m a" , "A 2_1/m 2/m 2/a" , "Amma" , "cab" , Bravais::A, 8, 300},
{ 63, "D2h^17", "-A 2 2a" , "A m a m" , "A 2_1/m 2/a 2/m" , "Amam" , "-cba" , Bravais::A, 8, 301},
{ 63, "D2h^17", "-B 2 2b" , "B b m m" , "B 2/b 2_1/m 2/m" , "Bbmm" , "bca" , Bravais::P, 8, 302},
{ 63, "D2h^17", "-B 2b 2" , "B m m b" , "B 2/m 2_1/m 2/b" , "Bmmb" , "a-cb" , Bravais::P, 8, 303},
{ 64, "D2h^18", "-C 2bc 2" , "C m c e" , "C 2/m 2/c 2_1/e" , "Cmce" , "" , Bravais::C, 8, 304},
{ 64, "D2h^18", "-C 2bc 2bc" , "C c m e" , "C 2/c 2/m 2_1/e" , "Ccme" , "ba-c" , Bravais::C, 8, 305},
{ 64, "D2h^18", "-A 2ac 2ac" , "A e m a" , "A 2_1/e 2/m 2/a" , "Aema" , "cab" , Bravais::A, 8, 306},
{ 64, "D2h^18", "-A 2 2ac" , "A e a m" , "A 2_1/e 2/a 2/m" , "Aeam" , "-cba" , Bravais::A, 8, 307},
{ 64, "D2h^18", "-B 2 2bc" , "B b e m" , "B 2/b 2_1/e 2/m" , "Bbem" , "bca" , Bravais::P, 8, 308},
{ 64, "D2h^18", "-B 2bc 2" , "B m e b" , "B 2/m 2_1/e 2/b" , "Bmeb" , "a-cb" , Bravais::P, 8, 309},
{ 65, "D2h^19", "-C 2 2" , "C m m m" , "C 2/m 2/m 2/m" , "Cmmm" , "" , Bravais::C, 8, 310},
{ 65, "D2h^19", "-A 2 2" , "A m m m" , "A 2/m 2/m 2/m" , "Ammm" , "cab" , Bravais::A, 8, 311},
{ 65, "D2h^19", "-B 2 2" , "B m m m" , "B 2/m 2/m 2/m" , "Bmmm" , "bca" , Bravais::P, 8, 312},
{ 66, "D2h^20", "-C 2 2c" , "C c c m" , "C 2/c 2/c 2/m" , "Cccm" , "" , Bravais::C, 8, 313},
{ 66, "D2h^20", "-A 2a 2" , "A m a a" , "A 2/m 2/a 2/a" , "Amaa" , "cab" , Bravais::A, 8, 314},
{ 66, "D2h^20", "-B 2b 2b" , "B b m b" , "B 2/b 2/m 2/b" , "Bbmb" , "bca" , Bravais::P, 8, 315},
{ 67, "D2h^21", "-C 2b 2" , "C m m e" , "C 2/m 2/m 2/e" , "Cmme" , "" , Bravais::C, 8, 316},
{ 67, "D2h^21", "-C 2b 2b" , "C m m e" , "C 2/m 2/m 2/e" , "Cmme" , "ba-c" , Bravais::C, 8, 317},
{ 67, "D2h^21", "-A 2c 2c" , "A e m m" , "A 2/e 2/m 2/m" , "Aemm" , "cab" , Bravais::A, 8, 318},
{ 67, "D2h^21", "-A 2 2c" , "A e m m" , "A 2/e 2/m 2/m" , "Aemm" , "-cba" , Bravais::A, 8, 319},
{ 67, "D2h^21", "-B 2 2c" , "B m e m" , "B 2/m 2/e 2/m" , "Bmem" , "bca" , Bravais::P, 8, 320},
{ 67, "D2h^21", "-B 2c 2" , "B m e m" , "B 2/m 2/e 2/m" , "Bmem" , "a-cb" , Bravais::P, 8, 321},
{ 68, "D2h^22", "C 2 2 -1bc" , "C c c e" , "C 2/c 2/c 2/e" , "Ccce" , "1" , Bravais::C, 8, 322},
{ 68, "D2h^22", "-C 2b 2bc" , "C c c e" , "C 2/c 2/c 2/e" , "Ccce" , "2" , Bravais::C, 8, 323},
{ 68, "D2h^22", "C 2 2 -1bc" , "C c c e" , "C 2/c 2/c 2/e" , "Ccce" , "1ba-c", Bravais::C, 8, 324},
{ 68, "D2h^22", "-C 2b 2c" , "C c c e" , "C 2/c 2/c 2/e" , "Ccce" , "2ba-c", Bravais::C, 8, 325},
{ 68, "D2h^22", "A 2 2 -1ac" , "A e a a" , "A 2/e 2/a 2/a" , "Aeaa" , "1cab" , Bravais::A, 8, 326},
{ 68, "D2h^22", "-A 2a 2c" , "A e a a" , "A 2/e 2/a 2/a" , "Aeaa" , "2cab" , Bravais::A, 8, 327},
{ 68, "D2h^22", "A 2 2 -1ac" , "A e a a" , "A 2/e 2/a 2/a" , "Aeaa" , "1-cba", Bravais::A, 8, 328},
{ 68, "D2h^22", "-A 2ac 2c" , "A e a a" , "A 2/e 2/a 2/a" , "Aeaa" , "2-cba", Bravais::A, 8, 329},
{ 68, "D2h^22", "B 2 2 -1bc" , "B b e b" , "B 2/b 2/e 2/b" , "Bbeb" , "1bca" , Bravais::P, 8, 330},
{ 68, "D2h^22", "-B 2bc 2b" , "B b c b" , "B 2/b 2/e 2/b" , "Bbcb" , "2bca" , Bravais::P, 8, 331},
{ 68, "D2h^22", "B 2 2 -1bc" , "B b e b" , "B 2/b 2/e 2/b" , "Bbeb" , "1a-cb", Bravais::P, 8, 332},
{ 68, "D2h^22", "-B 2b 2bc" , "B b e b" , "B 2/b 2/e 2/b" , "Bbeb" , "2a-cb", Bravais::P, 8, 333},
{ 69, "D2h^23", "-F 2 2" , "F m m m" , "F 2/m 2/m 2/m" , "Fmmm" , "" , Bravais::F, 8, 334},
{ 70, "D2h^24", "F 2 2 -1d" , "F d d d" , "F 2/d 2/d 2/d" , "Fddd" , "1" , Bravais::F, 8, 335},
{ 70, "D2h^24", "-F 2uv 2vw" , "F d d d" , "F 2/d 2/d 2/d" , "Fddd" , "2" , Bravais::F, 8, 336},
{ 71, "D2h^25", "-I 2 2" , "I m m m" , "I 2/m 2/m 2/m" , "Immm" , "" , Bravais::I, 8, 337},
{ 72, "D2h^26", "-I 2 2c" , "I b a m" , "I 2/b 2/a 2/m" , "Ibam" , "" , Bravais::I, 8, 338},
{ 72, "D2h^26", "-I 2a 2" , "I m c b" , "I 2/m 2/c 2/b" , "Imcb" , "cab" , Bravais::I, 8, 339},
{ 72, "D2h^26", "-I 2b 2b" , "I c m a" , "I 2/c 2/m 2/a" , "Icma" , "bca" , Bravais::I, 8, 340},
{ 73, "D2h^27", "-I 2b 2c" , "I b c a" , "I 2/b 2/c 2/a" , "Ibca" , "" , Bravais::I, 8, 341},
{ 73, "D2h^27", "-I 2a 2b" , "I c a b" , "I 2/c 2/a 2/b" , "Icab" , "ba-c" , Bravais::I, 8, 342},
{ 74, "D2h^28", "-I 2b 2" , "I m m a" , "I 2/m 2/m 2/a" , "Imma" , "" , Bravais::I, 8, 343},
{ 74, "D2h^28", "-I 2a 2a" , "I m m b" , "I 2/m 2/m 2/b" , "Immb" , "ba-c" , Bravais::I, 8, 344},
{ 74, "D2h^28", "-I 2c 2c" , "I b m m" , "I 2/b 2/m 2/m" , "Ibmm" , "cab" , Bravais::I, 8, 345},
{ 74, "D2h^28", "-I 2 2b" , "I c m m" , "I 2/c 2/m 2/m" , "Icmm" , "-cba" , Bravais::I, 8, 346},
{ 74, "D2h^28", "-I 2 2a" , "I m c m" , "I 2/m 2/c 2/m" , "Imcm" , "bca" , Bravais::I, 8, 347},
{ 74, "D2h^28", "-I 2c 2" , "I m a m" , "I 2/m 2/a 2/m" , "Imam" , "a-cb" , Bravais::I, 8, 348},
{ 75, "C4^1" , "P 4" , "P 4" , "P 4" , "P4" , "" , Bravais::P, 9, 349},
{ 76, "C4^2" , "P 4w" , "P 4_1" , "P 4_1" , "P4_1" , "" , Bravais::P, 9, 350},
{ 77, "C4^3" , "P 4c" , "P 4_2" , "P 4_2" , "P4_2" , "" , Bravais::P, 9, 351},
{ 78, "C4^4" , "P 4cw" , "P 4_3" , "P 4_3" , "P4_3" , "" , Bravais::P, 9, 352},
{ 79, "C4^5" , "I 4" , "I 4" , "I 4" , "I4" , "" , Bravais::I, 9, 353},
{ 80, "C4^6" , "I 4bw" , "I 4_1" , "I 4_1" , "I4_1" , "" , Bravais::I, 9, 354},
{ 81, "S4^1" , "P -4" , "P -4" , "P -4" , "P-4" , "" , Bravais::P, 10, 355},
{ 82, "S4^2" , "I -4" , "I -4" , "I -4" , "I-4" , "" , Bravais::I, 10, 356},
{ 83, "C4h^1" , "-P 4" , "P 4/m" , "P 4/m" , "P4/m" , "" , Bravais::P, 11, 357},
{ 84, "C4h^2" , "-P 4c" , "P 4_2/m" , "P 4_2/m" , "P4_2/m" , "" , Bravais::P, 11, 358},
{ 85, "C4h^3" , "P 4ab -1ab" , "P 4/n" , "P 4/n" , "P4/n" , "1" , Bravais::P, 11, 359},
{ 85, "C4h^3" , "-P 4a" , "P 4/n" , "P 4/n" , "P4/n" , "2" , Bravais::P, 11, 360},
{ 86, "C4h^4" , "P 4n -1n" , "P 4_2/n" , "P 4_2/n" , "P4_2/n" , "1" , Bravais::P, 11, 361},
{ 86, "C4h^4" , "-P 4bc" , "P 4_2/n" , "P 4_2/n" , "P4_2/n" , "2" , Bravais::P, 11, 362},
{ 87, "C4h^5" , "-I 4" , "I 4/m" , "I 4/m" , "I4/m" , "" , Bravais::I, 11, 363},
{ 88, "C4h^6" , "I 4bw -1bw" , "I 4_1/a" , "I 4_1/a" , "I4_1/a" , "1" , Bravais::I, 11, 364},
{ 88, "C4h^6" , "-I 4ad" , "I 4_1/a" , "I 4_1/a" , "I4_1/a" , "2" , Bravais::I, 11, 365},
{ 89, "D4^1" , "P 4 2" , "P 4 2 2" , "P 4 2 2" , "P422" , "" , Bravais::P, 12, 366},
{ 90, "D4^2" , "P 4ab 2ab" , "P 4 2_1 2" , "P 4 2_1 2" , "P42_12" , "" , Bravais::P, 12, 367},
{ 91, "D4^3" , "P 4w 2c" , "P 4_1 2 2" , "P 4_1 2 2" , "P4_122" , "" , Bravais::P, 12, 368},
{ 92, "D4^4" , "P 4abw 2nw" , "P 4_1 2_1 2" , "P 4_1 2_1 2" , "P4_12_12" , "" , Bravais::P, 12, 369},
{ 93, "D4^5" , "P 4c 2" , "P 4_2 2 2" , "P 4_2 2 2" , "P4_222" , "" , Bravais::P, 12, 370},
{ 94, "D4^6" , "P 4n 2n" , "P 4_2 2_1 2" , "P 4_2 2_1 2" , "P4_22_12" , "" , Bravais::P, 12, 371},
{ 95, "D4^7" , "P 4cw 2c" , "P 4_3 2 2" , "P 4_3 2 2" , "P4_322" , "" , Bravais::P, 12, 372},
{ 96, "D4^8" , "P 4nw 2abw" , "P 4_3 2_1 2" , "P 4_3 2_1 2" , "P4_32_12" , "" , Bravais::P, 12, 373},
{ 97, "D4^9" , "I 4 2" , "I 4 2 2" , "I 4 2 2" , "I422" , "" , Bravais::I, 12, 374},
{ 98, "D4^10" , "I 4bw 2bw" , "I 4_1 2 2" , "I 4_1 2 2" , "I4_122" , "" , Bravais::I, 12, 375},
{ 99, "C4v^1" , "P 4 -2" , "P 4 m m" , "P 4 m m" , "P4mm" , "" , Bravais::P, 13, 376},
{100, "C4v^2" , "P 4 -2ab" , "P 4 b m" , "P 4 b m" , "P4bm" , "" , Bravais::P, 13, 377},
{101, "C4v^3" , "P 4c -2c" , "P 4_2 c m" , "P 4_2 c m" , "P4_2cm" , "" , Bravais::P, 13, 378},
{102, "C4v^4" , "P 4n -2n" , "P 4_2 n m" , "P 4_2 n m" , "P4_2nm" , "" , Bravais::P, 13, 379},
{103, "C4v^5" , "P 4 -2c" , "P 4 c c" , "P 4 c c" , "P4cc" , "" , Bravais::P, 13, 380},
{104, "C4v^6" , "P 4 -2n" , "P 4 n c" , "P 4 n c" , "P4nc" , "" , Bravais::P, 13, 381},
{105, "C4v^7" , "P 4c -2" , "P 4_2 m c" , "P 4_2 m c" , "P4_2mc" , "" , Bravais::P, 13, 382},
{106, "C4v^8" , "P 4c -2ab" , "P 4_2 b c" , "P 4_2 b c" , "P4_2bc" , "" , Bravais::P, 13, 383},
{107, "C4v^9" , "I 4 -2" , "I 4 m m" , "I 4 m m" , "I4mm" , "" , Bravais::I, 13, 384},
{108, "C4v^10", "I 4 -2c" , "I 4 c m" , "I 4 c m" , "I4cm" , "" , Bravais::I, 13, 385},
{109, "C4v^11", "I 4bw -2" , "I 4_1 m d" , "I 4_1 m d" , "I4_1md" , "" , Bravais::I, 13, 386},
{110, "C4v^12", "I 4bw -2c" , "I 4_1 c d" , "I 4_1 c d" , "I4_1cd" , "" , Bravais::I, 13, 387},
{111, "D2d^1" , "P -4 2" , "P -4 2 m" , "P -4 2 m" , "P-42m" , "" , Bravais::P, 14, 388},
{112, "D2d^2" , "P -4 2c" , "P -4 2 c" , "P -4 2 c" , "P-42c" , "" , Bravais::P, 14, 389},
{113, "D2d^3" , "P -4 2ab" , "P -4 2_1 m" , "P -4 2_1 m" , "P-42_1m" , "" , Bravais::P, 14, 390},
{114, "D2d^4" , "P -4 2n" , "P -4 2_1 c" , "P -4 2_1 c" , "P-42_1c" , "" , Bravais::P, 14, 391},
{115, "D2d^5" , "P -4 -2" , "P -4 m 2" , "P -4 m 2" , "P-4m2" , "" , Bravais::P, 14, 392},
{116, "D2d^6" , "P -4 -2c" , "P -4 c 2" , "P -4 c 2" , "P-4c2" , "" , Bravais::P, 14, 393},
{117, "D2d^7" , "P -4 -2ab" , "P -4 b 2" , "P -4 b 2" , "P-4b2" , "" , Bravais::P, 14, 394},
{118, "D2d^8" , "P -4 -2n" , "P -4 n 2" , "P -4 n 2" , "P-4n2" , "" , Bravais::P, 14, 395},
{119, "D2d^9" , "I -4 -2" , "I -4 m 2" , "I -4 m 2" , "I-4m2" , "" , Bravais::I, 14, 396},
{120, "D2d^10", "I -4 -2c" , "I -4 c 2" , "I -4 c 2" , "I-4c2" , "" , Bravais::I, 14, 397},
{121, "D2d^11", "I -4 2" , "I -4 2 m" , "I -4 2 m" , "I-42m" , "" , Bravais::I, 14, 398},
{122, "D2d^12", "I -4 2bw" , "I -4 2 d" , "I -4 2 d" , "I-42d" , "" , Bravais::I, 14, 399},
{123, "D4h^1" , "-P 4 2" , "P 4/m m m" , "P 4/m 2/m 2/m" , "P4/mmm" , "" , Bravais::P, 15, 400},
{124, "D4h^2" , "-P 4 2c" , "P 4/m c c" , "P 4/m 2/c 2/c" , "P4/mcc" , "" , Bravais::P, 15, 401},
{125, "D4h^3" , "P 4 2 -1ab" , "P 4/n b m" , "P 4/n 2/b 2/m" , "P4/nbm" , "1" , Bravais::P, 15, 402},
{125, "D4h^3" , "-P 4a 2b" , "P 4/n b m" , "P 4/n 2/b 2/m" , "P4/nbm" , "2" , Bravais::P, 15, 403},
{126, "D4h^4" , "P 4 2 -1n" , "P 4/n n c" , "P 4/n 2/n 2/c" , "P4/nnc" , "1" , Bravais::P, 15, 404},
{126, "D4h^4" , "-P 4a 2bc" , "P 4/n n c" , "P 4/n 2/n 2/c" , "P4/nnc" , "2" , Bravais::P, 15, 405},
{127, "D4h^5" , "-P 4 2ab" , "P 4/m b m" , "P 4/m 2_1/b m" , "P4/mbm" , "" , Bravais::P, 15, 406},
{128, "D4h^6" , "-P 4 2n" , "P 4/m n c" , "P 4/m 2_1/n c" , "P4/mnc" , "" , Bravais::P, 15, 407},
{129, "D4h^7" , "P 4ab 2ab -1ab" , "P 4/n m m" , "P 4/n 2_1/m m" , "P4/nmm" , "1" , Bravais::P, 15, 408},
{129, "D4h^7" , "-P 4a 2a" , "P 4/n m m" , "P 4/n 2_1/m m" , "P4/nmm" , "2" , Bravais::P, 15, 409},
{130, "D4h^8" , "P 4ab 2n -1ab" , "P 4/n c c" , "P 4/n 2_1/c c" , "P4/ncc" , "1" , Bravais::P, 15, 410},
{130, "D4h^8" , "-P 4a 2ac" , "P 4/n c c" , "P 4/n 2_1/c c" , "P4/ncc" , "2" , Bravais::P, 15, 411},
{131, "D4h^9" , "-P 4c 2" , "P 4_2/m m c" , "P 4_2/m 2/m 2/c" , "P4_2/mmc" , "" , Bravais::P, 15, 412},
{132, "D4h^10", "-P 4c 2c" , "P 4_2/m c m" , "P 4_2/m 2/c 2/m" , "P4_2/mcm" , "" , Bravais::P, 15, 413},
{133, "D4h^11", "P 4n 2c -1n" , "P 4_2/n b c" , "P 4_2/n 2/b 2/c" , "P4_2/nbc" , "1" , Bravais::P, 15, 414},
{133, "D4h^11", "-P 4ac 2b" , "P 4_2/n b c" , "P 4_2/n 2/b 2/c" , "P4_2/nbc" , "2" , Bravais::P, 15, 415},
{134, "D4h^12", "P 4n 2 -1n" , "P 4_2/n n m" , "P 4_2/n 2/n 2/m" , "P4_2/nnm" , "1" , Bravais::P, 15, 416},
{134, "D4h^12", "-P 4ac 2bc" , "P 4_2/n n m" , "P 4_2/n 2/n 2/m" , "P4_2/nnm" , "2" , Bravais::P, 15, 417},
{135, "D4h^13", "-P 4c 2ab" , "P 4_2/m b c" , "P 4_2/m 2_1/b 2/c" , "P4_2/mbc" , "" , Bravais::P, 15, 418},
{136, "D4h^14", "-P 4n 2n" , "P 4_2/m n m" , "P 4_2/m 2_1/n 2/m" , "P4_2/mnm" , "" , Bravais::P, 15, 419},
{137, "D4h^15", "P 4n 2n -1n" , "P 4_2/n m c" , "P 4_2/n 2_1/m 2/c" , "P4_2/nmc" , "1" , Bravais::P, 15, 420},
{137, "D4h^15", "-P 4ac 2a" , "P 4_2/n m c" , "P 4_2/n 2_1/m 2/c" , "P4_2/nmc" , "2" , Bravais::P, 15, 421},
{138, "D4h^16", "P 4n 2ab -1n" , "P 4_2/n c m" , "P 4_2/n 2_1/c 2/m" , "P4_2/ncm" , "1" , Bravais::P, 15, 422},
{138, "D4h^16", "-P 4ac 2ac" , "P 4_2/n c m" , "P 4_2/n 2_1/c 2/m" , "P4_2/ncm" , "2" , Bravais::P, 15, 423},
{139, "D4h^17", "-I 4 2" , "I 4/m m m" , "I 4/m 2/m 2/m" , "I4/mmm" , "" , Bravais::I, 15, 424},
{140, "D4h^18", "-I 4 2c" , "I 4/m c m" , "I 4/m 2/c 2/m" , "I4/mcm" , "" , Bravais::I, 15, 425},
{141, "D4h^19", "I 4bw 2bw -1bw" , "I 4_1/a m d" , "I 4_1/a 2/m 2/d" , "I4_1/amd" , "1" , Bravais::I, 15, 426},
{141, "D4h^19", "-I 4bd 2" , "I 4_1/a m d" , "I 4_1/a 2/m 2/d" , "I4_1/amd" , "2" , Bravais::I, 15, 427},
{142, "D4h^20", "I 4bw 2aw -1bw" , "I 4_1/a c d" , "I 4_1/a 2/c 2/d" , "I4_1/acd" , "1" , Bravais::I, 15, 428},
{142, "D4h^20", "-I 4bd 2c" , "I 4_1/a c d" , "I 4_1/a 2/c 2/d" , "I4_1/acd" , "2" , Bravais::I, 15, 429},
{143, "C3^1" , "P 3" , "P 3" , "P 3" , "P3" , "" , Bravais::P, 16, 430},
{144, "C3^2" , "P 31" , "P 3_1" , "P 3_1" , "P3_1" , "" , Bravais::P, 16, 431},
{145, "C3^3" , "P 32" , "P 3_2" , "P 3_2" , "P3_2" , "" , Bravais::P, 16, 432},
{146, "C3^4" , "R 3" , "R 3" , "R 3" , "R3" , "H" , Bravais::R, 16, 433},
{146, "C3^4" , "P 3*" , "R 3" , "R 3" , "R3" , "R" , Bravais::P, 16, 434},
{147, "C3i^1" , "-P 3" , "P -3" , "P -3" , "P-3" , "" , Bravais::P, 17, 435},
{148, "C3i^2" , "-R 3" , "R -3" , "R -3" , "R-3" , "H" , Bravais::R, 17, 436},
{148, "C3i^2" , "-P 3*" , "R -3" , "R -3" , "R-3" , "R" , Bravais::P, 17, 437},
{149, "D3^1" , "P 3 2" , "P 3 1 2" , "P 3 1 2" , "P312" , "" , Bravais::P, 18, 438},
{150, "D3^2" , "P 3 2\"" , "P 3 2 1" , "P 3 2 1" , "P321" , "" , Bravais::P, 18, 439},
{151, "D3^3" , "P 31 2c (0 0 1)" , "P 3_1 1 2" , "P 3_1 1 2" , "P3_112" , "" , Bravais::P, 18, 440},
{152, "D3^4" , "P 31 2\"" , "P 3_1 2 1" , "P 3_1 2 1" , "P3_121" , "" , Bravais::P, 18, 441},
{153, "D3^5" , "P 32 2c (0 0 -1)", "P 3_2 1 2" , "P 3_2 1 2" , "P3_212" , "" , Bravais::P, 18, 442},
{154, "D3^6" , "P 32 2\"" , "P 3_2 2 1" , "P 3_2 2 1" , "P3_221" , "" , Bravais::P, 18, 443},
{155, "D3^7" , "R 3 2\"" , "R 3 2" , "R 3 2" , "R32" , "H" , Bravais::R, 18, 444},
{155, "D3^7" , "P 3* 2" , "R 3 2" , "R 3 2" , "R32" , "R" , Bravais::P, 18, 445},
{156, "C3v^1" , "P 3 -2\"" , "P 3 m 1" , "P 3 m 1" , "P3m1" , "" , Bravais::P, 19, 446},
{157, "C3v^2" , "P 3 -2" , "P 3 1 m" , "P 3 1 m" , "P31m" , "" , Bravais::P, 19, 447},
{158, "C3v^3" , "P 3 -2\"c" , "P 3 c 1" , "P 3 c 1" , "P3c1" , "" , Bravais::P, 19, 448},
{159, "C3v^4" , "P 3 -2c" , "P 3 1 c" , "P 3 1 c" , "P31c" , "" , Bravais::P, 19, 449},
{160, "C3v^5" , "R 3 -2\"" , "R 3 m" , "R 3 m" , "R3m" , "H" , Bravais::R, 19, 450},
{160, "C3v^5" , "P 3* -2" , "R 3 m" , "R 3 m" , "R3m" , "R" , Bravais::P, 19, 451},
{161, "C3v^6" , "R 3 -2\"c" , "R 3 c" , "R 3 c" , "R3c" , "H" , Bravais::R, 19, 452},
{161, "C3v^6" , "P 3* -2n" , "R 3 c" , "R 3 c" , "R3c" , "R" , Bravais::P, 19, 453},
{162, "D3d^1" , "-P 3 2" , "P -3 1 m" , "P -3 1 2/m" , "P-31m" , "" , Bravais::P, 20, 454},
{163, "D3d^2" , "-P 3 2c" , "P -3 1 c" , "P -3 1 2/c" , "P-31c" , "" , Bravais::P, 20, 455},
{164, "D3d^3" , "-P 3 2\"" , "P -3 m 1" , "P -3 2/m 1" , "P-3m1" , "" , Bravais::P, 20, 456},
{165, "D3d^4" , "-P 3 2\"c" , "P -3 c 1" , "P -3 2/c 1" , "P-3c1" , "" , Bravais::P, 20, 457},
{166, "D3d^5" , "-R 3 2\"" , "R -3 m" , "R -3 2/m" , "R-3m" , "H" , Bravais::R, 20, 458},
{166, "D3d^5" , "-P 3* 2" , "R -3 m" , "R -3 2/m" , "R-3m" , "R" , Bravais::P, 20, 459},
{167, "D3d^6" , "-R 3 2\"c" , "R -3 c" , "R -3 2/c" , "R-3c" , "H" , Bravais::R, 20, 460},
{167, "D3d^6" , "-P 3* 2n" , "R -3 c" , "R -3 2/c" , "R-3c" , "R" , Bravais::P, 20, 461},
{168, "C6^1" , "P 6" , "P 6" , "P 6" , "P6" , "" , Bravais::P, 21, 462},
{169, "C6^2" , "P 61" , "P 6_1" , "P 6_1" , "P6_1" , "" , Bravais::P, 21, 463},
{170, "C6^3" , "P 65" , "P 6_5" , "P 6_5" , "P6_5" , "" , Bravais::P, 21, 464},
{171, "C6^4" , "P 62" , "P 6_2" , "P 6_2" , "P6_2" , "" , Bravais::P, 21, 465},
{172, "C6^5" , "P 64" , "P 6_4" , "P 6_4" , "P6_4" , "" , Bravais::P, 21, 466},
{173, "C6^6" , "P 6c" , "P 6_3" , "P 6_3" , "P6_3" , "" , Bravais::P, 21, 467},
{174, "C3h^1" , "P -6" , "P -6" , "P -6" , "P-6" , "" , Bravais::P, 22, 468},
{175, "C6h^1" , "-P 6" , "P 6/m" , "P 6/m" , "P6/m" , "" , Bravais::P, 23, 469},
{176, "C6h^2" , "-P 6c" , "P 6_3/m" , "P 6_3/m" , "P6_3/m" , "" , Bravais::P, 23, 470},
{177, "D6^1" , "P 6 2" , "P 6 2 2" , "P 6 2 2" , "P622" , "" , Bravais::P, 24, 471},
{178, "D6^2" , "P 61 2 (0 0 -1)" , "P 6_1 2 2" , "P 6_1 2 2" , "P6_122" , "" , Bravais::P, 24, 472},
{179, "D6^3" , "P 65 2 (0 0 1)" , "P 6_5 2 2" , "P 6_5 2 2" , "P6_522" , "" , Bravais::P, 24, 473},
{180, "D6^4" , "P 62 2c (0 0 1)" , "P 6_2 2 2" , "P 6_2 2 2" , "P6_222" , "" , Bravais::P, 24, 474},
{181, "D6^5" , "P 64 2c (0 0 -1)", "P 6_4 2 2" , "P 6_4 2 2" , "P6_422" , "" , Bravais::P, 24, 475},
{182, "D6^6" , "P 6c 2c" , "P 6_3 2 2" , "P 6_3 2 2" , "P6_322" , "" , Bravais::P, 24, 476},
{183, "C6v^1" , "P 6 -2" , "P 6 m m" , "P 6 m m" , "P6mm" , "" , Bravais::P, 25, 477},
{184, "C6v^2" , "P 6 -2c" , "P 6 c c" , "P 6 c c" , "P6cc" , "" , Bravais::P, 25, 478},
{185, "C6v^3" , "P 6c -2" , "P 6_3 c m" , "P 6_3 c m" , "P6_3cm" , "" , Bravais::P, 25, 479},
{186, "C6v^4" , "P 6c -2c" , "P 6_3 m c" , "P 6_3 m c" , "P6_3mc" , "" , Bravais::P, 25, 480},
{187, "D3h^1" , "P -6 2" , "P -6 m 2" , "P -6 m 2" , "P-6m2" , "" , Bravais::P, 26, 481},
{188, "D3h^2" , "P -6c 2" , "P -6 c 2" , "P -6 c 2" , "P-6c2" , "" , Bravais::P, 26, 482},
{189, "D3h^3" , "P -6 -2" , "P -6 2 m" , "P -6 2 m" , "P-62m" , "" , Bravais::P, 26, 483},
{190, "D3h^4" , "P -6c -2c" , "P -6 2 c" , "P -6 2 c" , "P-62c" , "" , Bravais::P, 26, 484},
{191, "D6h^1" , "-P 6 2" , "P 6/m m m" , "P 6/m 2/m 2/m" , "P6/mmm" , "" , Bravais::P, 27, 485},
{192, "D6h^2" , "-P 6 2c" , "P 6/m c c" , "P 6/m 2/c 2/c" , "P6/mcc" , "" , Bravais::P, 27, 486},
{193, "D6h^3" , "-P 6c 2" , "P 6_3/m c m" , "P 6_3/m 2/c 2/m" , "P6_3/mcm" , "" , Bravais::P, 27, 487},
{194, "D6h^4" , "-P 6c 2c" , "P 6_3/m m c" , "P 6_3/m 2/m 2/c" , "P6_3/mmc" , "" , Bravais::P, 27, 488},
{195, "T^1" , "P 2 2 3" , "P 2 3" , "P 2 3" , "P23" , "" , Bravais::P, 28, 489},
{196, "T^2" , "F 2 2 3" , "F 2 3" , "F 2 3" , "F23" , "" , Bravais::F, 28, 490},
{197, "T^3" , "I 2 2 3" , "I 2 3" , "I 2 3" , "I23" , "" , Bravais::I, 28, 491},
{198, "T^4" , "P 2ac 2ab 3" , "P 2_1 3" , "P 2_1 3" , "P2_13" , "" , Bravais::P, 28, 492},
{199, "T^5" , "I 2b 2c 3" , "I 2_1 3" , "I 2_1 3" , "I2_13" , "" , Bravais::I, 28, 493},
{200, "Th^1" , "-P 2 2 3" , "P m -3" , "P 2/m -3" , "Pm-3" , "" , Bravais::P, 29, 494},
{201, "Th^2" , "P 2 2 3 -1n" , "P n -3" , "P 2/n -3" , "Pn-3" , "1" , Bravais::P, 29, 495},
{201, "Th^2" , "-P 2ab 2bc 3" , "P n -3" , "P 2/n -3" , "Pn-3" , "2" , Bravais::P, 29, 496},
{202, "Th^3" , "-F 2 2 3" , "F m -3" , "F 2/m -3" , "Fm-3" , "" , Bravais::F, 29, 497},
{203, "Th^4" , "F 2 2 3 -1d" , "F d -3" , "F 2/d -3" , "Fd-3" , "1" , Bravais::F, 29, 498},
{203, "Th^4" , "-F 2uv 2vw 3" , "F d -3" , "F 2/d -3" , "Fd-3" , "2" , Bravais::F, 29, 499},
{204, "Th^5" , "-I 2 2 3" , "I m -3" , "I 2/m -3" , "Im-3" , "" , Bravais::I, 29, 500},
{205, "Th^6" , "-P 2ac 2ab 3" , "P a -3" , "P 2_1/a -3" , "Pa-3" , "" , Bravais::P, 29, 501},
{206, "Th^7" , "-I 2b 2c 3" , "I a -3" , "I 2_1/a -3" , "Ia-3" , "" , Bravais::I, 29, 502},
{207, "O^1" , "P 4 2 3" , "P 4 3 2" , "P 4 3 2" , "P432" , "" , Bravais::P, 30, 503},
{208, "O^2" , "P 4n 2 3" , "P 4_2 3 2" , "P 4_2 3 2" , "P4_232" , "" , Bravais::P, 30, 504},
{209, "O^3" , "F 4 2 3" , "F 4 3 2" , "F 4 3 2" , "F432" , "" , Bravais::F, 30, 505},
{210, "O^4" , "F 4d 2 3" , "F 4_1 3 2" , "F 4_1 3 2" , "F4_132" , "" , Bravais::F, 30, 506},
{211, "O^5" , "I 4 2 3" , "I 4 3 2" , "I 4 3 2" , "I432" , "" , Bravais::I, 30, 507},
{212, "O^6" , "P 4acd 2ab 3" , "P 4_3 3 2" , "P 4_3 3 2" , "P4_332" , "" , Bravais::P, 30, 508},
{213, "O^7" , "P 4bd 2ab 3" , "P 4_1 3 2" , "P 4_1 3 2" , "P4_132" , "" , Bravais::P, 30, 509},
{214, "O^8" , "I 4bd 2c 3" , "I 4_1 3 2" , "I 4_1 3 2" , "I4_132" , "" , Bravais::I, 30, 510},
{215, "Td^1" , "P -4 2 3" , "P -4 3 m" , "P -4 3 m" , "P-43m" , "" , Bravais::P, 31, 511},
{216, "Td^2" , "F -4 2 3" , "F -4 3 m" , "F -4 3 m" , "F-43m" , "" , Bravais::F, 31, 512},
{217, "Td^3" , "I -4 2 3" , "I -4 3 m" , "I -4 3 m" , "I-43m" , "" , Bravais::I, 31, 513},
{218, "Td^4" , "P -4n 2 3" , "P -4 3 n" , "P -4 3 n" , "P-43n" , "" , Bravais::P, 31, 514},
{219, "Td^5" , "F -4c 2 3" , "F -4 3 c" , "F -4 3 c" , "F-43c" , "" , Bravais::F, 31, 515},
{220, "Td^6" , "I -4bd 2c 3" , "I -4 3 d" , "I -4 3 d" , "I-43d" , "" , Bravais::I, 31, 516},
{221, "Oh^1" , "-P 4 2 3" , "P m -3 m" , "P 4/m -3 2/m" , "Pm-3m" , "" , Bravais::P, 32, 517},
{222, "Oh^2" , "P 4 2 3 -1n" , "P n -3 n" , "P 4/n -3 2/n" , "Pn-3n" , "1" , Bravais::P, 32, 518},
{222, "Oh^2" , "-P 4a 2bc 3" , "P n -3 n" , "P 4/n -3 2/n" , "Pn-3n" , "2" , Bravais::P, 32, 519},
{223, "Oh^3" , "-P 4n 2 3" , "P m -3 n" , "P 4_2/m -3 2/n" , "Pm-3n" , "" , Bravais::P, 32, 520},
{224, "Oh^4" , "P 4n 2 3 -1n" , "P n -3 m" , "P 4_2/n -3 2/m" , "Pn-3m" , "1" , Bravais::P, 32, 521},
{224, "Oh^4" , "-P 4bc 2bc 3" , "P n -3 m" , "P 4_2/n -3 2/m" , "Pn-3m" , "2" , Bravais::P, 32, 522},
{225, "Oh^5" , "-F 4 2 3" , "F m -3 m" , "F 4/m -3 2/m" , "Fm-3m" , "" , Bravais::F, 32, 523},
{226, "Oh^6" , "-F 4c 2 3" , "F m -3 c" , "F 4/m -3 2/c" , "Fm-3c" , "" , Bravais::F, 32, 524},
{227, "Oh^7" , "F 4d 2 3 -1d" , "F d -3 m" , "F 4_1/d -3 2/m" , "Fd-3m" , "1" , Bravais::F, 32, 525},
{227, "Oh^7" , "-F 4vw 2vw 3" , "F d -3 m" , "F 4_1/d -3 2/m" , "Fd-3m" , "2" , Bravais::F, 32, 526},
{228, "Oh^8" , "F 4d 2 3 -1cd" , "F d -3 c" , "F 4_1/d -3 2/c" , "Fd-3c" , "1" , Bravais::F, 32, 527},
{228, "Oh^8" , "-F 4cvw 2vw 3" , "F d -3 c" , "F 4_1/d -3 2/c" , "Fd-3c" , "2" , Bravais::F, 32, 528},
{229, "Oh^9" , "-I 4 2 3" , "I m -3 m" , "I 4/m -3 2/m" , "Im-3m" , "" , Bravais::I, 32, 529},
{230, "Oh^10" , "-I 4bd 2c 3" , "I a -3 d" , "I 4_1/a -3 2/d" , "Ia-3d" , "" , Bravais::I, 32, 530},
};
bool brille::hall_number_ok(const int h) {return h>0 && h<531;}
int brille::international_number_to_hall_number(const int n, const std::string& c){
if (n>=0 && n<230) for (int i=1; i<531; i++){
Spacegroup spg(ALL_SPACEGROUPS[i]);
if (n==spg.number && (0==c.size() || 0==c.compare(spg.choice))) return i;
}
return -1;
}
int brille::international_string_to_hall_number(const std::string& n, const std::string& c){
for (int i=1; i<531; i++) {
Spacegroup spg(ALL_SPACEGROUPS[i]);
// now check for matching international table names
if( (0==c.size() || 0==c.compare(spg.choice)) &&
( 0==n.compare(spg.international)
|| 0==n.compare(spg.international_full)
|| 0==n.compare(spg.international_short))
) return i;
}
return 0; // no matching strings
}
int brille::hall_symbol_to_hall_number(const std::string& hsymbol){
for (int i=1; i<531; i++){
Spacegroup spg(ALL_SPACEGROUPS[i]);
// only accept exact matches
if (0==hsymbol.compare(spg.hall_symbol)) return i;
}
return 0; // no exact matches
}
// When we don't know if we're searching for a Hall Symbol or
// International Table Name/Symbol search for either, starting with Hall symbols
int brille::string_to_hall_number(const std::string& str, const std::string& ch){
int tmp = brille::hall_symbol_to_hall_number(str);
if (!tmp) tmp = brille::international_string_to_hall_number(str, ch);
return tmp;
}
void Spacegroup::set_from_hall_number(const int hn){
Spacegroup spg(ALL_SPACEGROUPS[brille::hall_number_ok(hn) ? hn : 0]);
this->number = spg.number;
this->schoenflies = spg.schoenflies;
this->hall_symbol = spg.hall_symbol;
this->international = spg.international;
this->international_full = spg.international_full;
this->international_short = spg.international_short;
this->choice = spg.choice;
this->bravais = spg.bravais;
this->pointgroup_number = spg.pointgroup_number;
this->hall_number = spg.hall_number;
}
Symmetry Spacegroup::get_spacegroup_symmetry() const {
HallSymbol hs(this->hall_symbol);
Symmetry generators = hs.get_generators();
Symmetry fullsym = generators.generate();
return fullsym;
}
PointSymmetry Spacegroup::get_pointgroup_symmetry(const int time_reversal) const{
Symmetry sym = this->get_spacegroup_symmetry();
std::vector<std::array<int,9>> uniqrots = get_unique_rotations(sym.getallr(), time_reversal);
return PointSymmetry(uniqrots);
}