/
identities.py
165 lines (145 loc) · 6.34 KB
/
identities.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Jul 1 11:09:23 2019
@author: Kirby Urner
"""
"""
From David Koski's paper:
Revisiting R.B. Fuller's S & E Modules
--------
The concentric hierarchy can be described in terms of
phi-scaled S modules:
Tetrahedron: 21S + 5s3 = 5S3 + 1S = 1S6 + 1S3
Cube : 72S + 15s3 = 15S3 + 3S = 3S6 + 3S3
Octahedron : 84S + 20s3 = 20S3 + 4S = 4S6 + 4S3
Rh Triac : 105S + 25s3 = 25S3 + 5S = 5S6 + 5S3 (volume = 5)
Rh Dodec : 126S + 30s3 = 30S3 + 6S = 6S6 + 6S3
Pent Dodeca: 348E + 84e3
Icosahedron: 100E3 + 20E
VE : 20
SuperRT : 20 * S3
--------
On-line: http://coffeeshopsnet.blogspot.com/2017/06/koski-paper.html
"""
from math import sqrt as rt2
import pandas as pd
import numpy as np
shapes = pd.Series(
np.array(["SuperRT",
"Cubocta",
"Icosa",
"P Dodeca",
"Rh Dodeca",
"RT5+",
"RT5",
"Octa",
"Cube",
"Sm Icosa",
"Sm VE",
"Tetra",
"Emod3",
"Emod",
"emod3",
"Tmod",
"Amod",
"Bmod",
"Smod3",
"Smod",
"smod3"], dtype=np.unicode_),
name="Shapes")
zeros = pd.Series(np.zeros((21,)), dtype=np.float64)
volumes_table = pd.DataFrame({"Volumes" : zeros,
"Comments": pd.Series(['']*21,
dtype=np.unicode_)
})
volumes_table.index = shapes
#%%
φ = (rt2(5)+1)/2 # golden ratio
S3 = rt2(9/8) # not to be confused with Smod
Smod = (φ **-5)/2 # home base Smod
smod3 = Smod * φ**-3 # small s, phi down
Smod3 = Smod * φ**3 # capital s, phi up
Smod6 = Smod3 * φ**3 # phi up yet again
cubocta = 20
SuperRT = S3 * cubocta
Octa = 4
Emod3 = SuperRT / 120 # Emod phi up
Emod = (rt2(2)/8) * (φ ** -3) # home base Emod
emod3 = Emod * φ ** -3 # Emod phi down
S_factor = Smod / Emod
T_factor = pow(3/2, 1/3) * rt2(2)/φ
SmallVE = 20 * 1/8 # half D edges (=R)
SkewIcosa = SmallVE * S_factor * S_factor
Smod_check = (Octa - SkewIcosa)/24
assert round(Smod,8) == round(Smod_check,8)
volumes_table.loc['SuperRT', "Volumes"] = SuperRT
volumes_table.loc['SuperRT', "Comments"] = "Emods RT phi-up, (Icosa, P Dodeca)"
volumes_table.loc['Cubocta', "Volumes"] = cubocta
volumes_table.loc['Cubocta', "Comments"] = "12 balls around 1"
volumes_table.loc['Icosa', "Volumes"] = 100*Emod3 + 20*Emod
volumes_table.loc['Icosa', "Comments"] = "Jitterbug first stop"
volumes_table.loc['P Dodeca', "Volumes"] = 348*Emod + 84*emod3
volumes_table.loc['P Dodeca', "Comments"] = "Icosahedron Dual"
volumes_table.loc['Rh Dodeca', "Volumes"] = 6*Smod6 + 6*Smod3
volumes_table.loc['Rh Dodeca', "Comments"] = "Space-filler, ball domain, (Cube, Octa)"
volumes_table.loc['RT5+', "Volumes"] = 120*Emod
volumes_table.loc['RT5+', "Comments"] = "Radius = 1.0000"
volumes_table.loc['RT5', "Volumes"] = 5*Smod6 + 5*Smod3
volumes_table.loc['RT5', "Comments"] = "Radius = 0.9994"
volumes_table.loc['Octa', "Volumes"] = 4*Smod6 + 4*Smod3
volumes_table.loc['Octa', "Comments"] = "Jitterbug 2nd stop, Cube dual"
volumes_table.loc['Cube', "Volumes"] = 3*Smod6 + 3*Smod3
volumes_table.loc['Cube', "Comments"] = "Duo-tet cube, Octa dual"
volumes_table.loc['Sm Icosa', "Volumes"] = SmallVE * S_factor * S_factor
volumes_table.loc['Sm Icosa', "Comments"] = "Faces flush with Octa"
volumes_table.loc['Sm VE', "Volumes"] = SmallVE
volumes_table.loc['Sm VE', "Comments"] = "Faces flush with Octa"
volumes_table.loc['Tetra', "Volumes"] = 5*Smod3 + Smod
volumes_table.loc['Tetra', "Comments"] = "Unit Volume"
volumes_table.loc['Emod3', "Volumes"] = Emod3
volumes_table.loc['Emod3', "Comments"] = "Emod phi up"
volumes_table.loc['Emod', "Volumes"] = Emod
volumes_table.loc['Emod', "Comments"] = "1/120th RT5+"
volumes_table.loc['emod3', "Volumes"] = emod3
volumes_table.loc['emod3', "Comments"] = "Emod phi down"
volumes_table.loc['Tmod', "Volumes"] = Emod * 1/T_factor**3 # 1/24
volumes_table.loc['Tmod', "Comments"] = "1/120th RT5"
volumes_table.loc['Amod', "Volumes"] = 1/24
volumes_table.loc['Amod', "Comments"] = "12 left + 12 right = Tetra"
volumes_table.loc['Bmod', "Volumes"] = 1/24
volumes_table.loc['Bmod', "Comments"] = "48A + 48B = Octa"
volumes_table.loc['Smod3', "Volumes"] = Smod3
volumes_table.loc['Smod3', "Comments"] = "Smod phi up"
volumes_table.loc['Smod', "Volumes" ] = Smod
volumes_table.loc['Smod', "Comments" ] = "Sm Icosa + 24 Smods = Octa"
volumes_table.loc['smod3', "Volumes"] = smod3
volumes_table.loc['smod3', "Comments"] = "Smod phi down"
def print_table():
print("Five VEs : {:10.6f}".format(480*Smod + 280*smod3))
print("SuperRT : {:10.6f}".format(SuperRT))
print("Cubocta : {:10.6f}".format(cubocta))
# print("Volume of Icosa : {:10.6f}".format(20 * 1/S_factor))
# print("Volume of Icosa : {:10.6f}".format(420 * Emod + 100 * emod3))
print("Icosa : {:10.6f}".format(100*Emod3 + 20*Emod))
print("P Dodeca : {:10.6f}".format(348*Emod + 84*emod3))
print("Rh Dodeca (RD): {:10.6f}".format(6*Smod6 + 6*Smod3))
print("RT5+ : {:10.6f}".format(120*Emod))
print("RT5 : {:10.6f}".format(5*Smod6 + 5*Smod3))
print("Octa : {:10.6f}".format(4*Smod6 + 4*Smod3))
print("Cube : {:10.6f}".format(3*Smod6 + 3*Smod3))
print("Skew Icosa : {:10.6f}".format(SmallVE * S_factor * S_factor))
print("Small VE : {:10.6f}".format(SmallVE))
print("Tetra : {:10.6f}".format(5*Smod3 + Smod))
print("-" * 20)
print("Emod3 : {:10.6f}".format(Emod3))
print("Emod : {:10.6f}".format(Emod))
print("emod3 : {:10.6f}".format(emod3))
print("Tmod : {:10.6f}".format(Emod*1/T_factor**3))
print("Smod6 : {:10.6f}".format(Smod6))
print("Smod3 : {:10.6f}".format(Smod3))
print("Smod : {:10.6f}".format(Smod))
print("Smod (check) : {:10.6f}".format(Smod_check))
print("smod3 : {:10.6f}".format(smod3))
if __name__ == "__main__":
print_table()