The code below, which I've shared before in an earlier draft, is meant to test mailman's Unicode abilities i.e. when I check the archives, is everything intact, font-wise etc. Thanks to two of my OST students for helping out. I18N is to be OST's theme at OSCON this year so I consider this work "on the clock" as we say. Kirby Urner O'Reilly School of Technology ====== """ Includes: PlaneNets (ПлейнНэт) from Synergetics for A, B, E, T, S Koski breakdowns of some shapes in E and S vols with phi scaling Euler volume, modified by Gerald de Jong http://www.grunch.net/synergetics/quadvols.html Kirby Urner (c) MIT License Министерство Глупых Походок Министерство образования """ from math import sqrt, hypot # sqrt: квадратный_корень class ПлейнНэт: """Любой шесть край тет в шаблоне описано в API нот""" def __init__(self, oa, ob, oc, ab, bc, ca): self.oa = oa self.ob = ob self.oc = oc self.ab = ab self.bc = bc self.ca = ca class Тетраэдр: """ Займет шесть края тетраэдра с лицами (а, б, г) (б, в, д) (с, а, е) (д, д, е) - объем возвращается если IVM и XYZ """ def __init__(self, a,b,c,d,e,f): self.a, self.a2 = a, a**2 self.b, self.b2 = b, b**2 self.c, self.c2 = c, c**2 self.d, self.d2 = d, d**2 self.e, self.e2 = e, e**2 self.f, self.f2 = f, f**2 def ivm_объем(self): return ((self._addopen()- self._addclosed() - self._addopposite())/2) ** 0.5 def xyz_объем(self): return sqrt(8/9) * self.ivm_volume() def _addopen(self): a2,b2,c2,d2,e2,f2 = self.a2, self.b2, self.c2, self.d2, self.e2, self.f2 sumval = f2*a2*b2 sumval += d2 * a2 * c2 sumval += a2 * b2 * e2 sumval += c2 * b2 * d2 sumval += e2 * c2 * a2 sumval += f2 * c2 * b2 sumval += e2 * d2 * a2 sumval += b2 * d2 * f2 sumval += b2 * e2 * f2 sumval += d2 * e2 * c2 sumval += a2 * f2 * e2 sumval += d2 * f2 * c2 return sumval def _addclosed(self): a2,b2,c2,d2,e2,f2 = self.a2, self.b2, self.c2, self.d2, self.e2, self.f2 sumval = a2 * b2 * d2 sumval += d2 * e2 * f2 sumval += b2 * c2 * e2 sumval += a2 * c2 * f2 return sumval def _addopposite(self): a2,b2,c2,d2,e2,f2 = self.a2, self.b2, self.c2, self.d2, self.e2, self.f2 sumval = a2 * e2 * (a2 + e2) sumval += b2 * f2 * (b2 + f2) sumval += c2 * d2 * (c2 + d2) return sumval φ = sqrt(5)/2 + 0.5 D = 1.0 R = D/2 def объем(net): return Тетраэдр(net.oa, net.ob, net.oc, net.ab, net.bc, net.ca ).ivm_объем() # Fig. 913.01 A Quanta Module # http://www.rwgrayprojects.com/synergetics/s09/figs/f1301.html a = D EF = a * sqrt(6) / 12 EC = a * sqrt(6) / 4 ED = a * sqrt(2) / 4 FC = a * sqrt(3) / 3 CD = a/2 DF = a * sqrt(3) / 6 Amod = ПлейнНэт(EF, EC, ED, FC, CD, DF) Avol = объем(Amod) print("Amod volume = :", Avol) # Fig. 916.01 B Quanta Module # http://www.rwgrayprojects.com/synergetics/s09/figs/f1601.html a = D EA = a * sqrt(2) / 2 EC = a/2 EB = a * sqrt(6) / 12 AC = a/2 CB = a * sqrt(2) / 4 BA = a * sqrt(6) / 4 Bmod = ПлейнНэт(EA, EC, EB, AC, CB, BA) Bvol = объем(Bmod) print("Bmod volume = :", Bvol) # Fig. 986.411A T & E Module # http://www.rwgrayprojects.com/synergetics/s09/figs/f86411a.html h = R OC = h OA = h * sqrt((5 - sqrt(5))/2) OB = h * sqrt((9 - 3 * sqrt(5))/2 ) CA = (h/2) * (sqrt(5) - 1) AB = h * sqrt(5 - 2 * sqrt(5)) BC = (h/2) * (3 - sqrt(5)) Emod = ПлейнНэт(OC, OA, OB, CA, AB, BC) Evol = объем(Emod) print("Emod volume = :", Evol) # Fig. 986.411A T & E Module # http://www.rwgrayprojects.com/synergetics/s09/figs/f86411a.html h = R * pow(2/3,1/3) * (φ / sqrt(2)) OC = h OA = h * sqrt((5 - sqrt(5))/2) OB = h * sqrt((9 - 3 * sqrt(5))/2 ) CA = (h/2) * (sqrt(5) - 1) AB = h * sqrt(5 - 2 * sqrt(5)) BC = (h/2) * (3 - sqrt(5)) Tmod = ПлейнНэт(OC, OA, OB, CA, AB, BC) Tvol = объем(Tmod) print("Tmod volume = :", Tvol) # Fig. 988.13A S Quanta Module Edge Lengths # http://www.rwgrayprojects.com/synergetics/s09/figs/f8813a.html a = D FG = (a/2) * sqrt(3) * sqrt(7-3*sqrt(5)) FE = a * sqrt(7 - 3*sqrt(5)) FH = (a/2) * (sqrt(5)-1) GE = (a/2) * sqrt(7 - 3*sqrt(5)) EH = (a/2) * (3 - sqrt(5)) HG = (a/2) * sqrt (7 - 3*sqrt(5)) Smod = ПлейнНэт(FG, FE, FH, GE, EH, HG) Svol = объем(Smod) print("Smod volume = :", Svol) # φ**=5 / 2 print("================") sFactor = Svol / Evol s3 = Svol * pow(φ, -3) s6 = Svol * pow(φ, -6) e3 = Evol * pow(φ, -3) E3 = Evol * pow(φ, 3) print("sFactor (Svol/Evol) = ", sFactor) print("================") BUvol = (20 * sFactor ** 2) LUvol = BUvol/8 # 60 * S + 20 * s3 print("BigUgly: {:10.7f}".format(BUvol)) print("SuperRT: {:10.7f}".format(120 * E3)) # ромбические триаконтаэдра # print("UnknownTet: {:10.7f}".format(20 * sFactor ** 1)) print("VE (edge 2): {:10.7f}".format(20 * sFactor ** 0)) # 420 * Svol + 100 * s3 print("Icosa (edge 2): {:10.7f}".format(20 * sFactor ** -1)) # 420 * Evol + 100 * e3 # print("BizzaroTet: {:10.7f}".format(20 * sFactor ** -2)) # 360 * Svol + 85 * s3 print("SmallGuy: {:10.7f}".format(20 * sFactor ** -3)) # 360 * Evol + 85 * e3 print("RD6: {:10.7f}".format((2*Avol + Bvol) * 4 * 12)) print("RT5+: {:10.7f}".format(120 * Evol)) # ромбические триаконтаэдра print("RT5: {:10.7f}".format(120 * Tvol)) # ромбические триаконтаэдра print("октаэдр (edge 2): {:10.7f}".format((Avol + Bvol) * 6 * 8)) # 6 ABs per face print("LittleUgly + 24 Smods: {:10.7f}".format(LUvol + 24 * Svol)) print("куб: {:10.7f}".format(267* s3 + 63 * s6)) # Тетраэдр + 6 1/8 октаэдр print("LittleUgly: {:10.7f}".format(LUvol)) print("VE faces in LittleUgly: {:10.7f}".format(LUvol * sFactor**-2)) print("Тетраэдр: {:10.7f}".format( 21 * Svol + 5 * s3)) import unittest class Test_Tetrahedron(unittest.TestCase): def test_unit_volume(self): tet = Тетраэдр(D, D, D, D, D, D).ivm_объем() self.assertAlmostEqual(tet, 1.0) def test_unit_volume2(self): tet = Тетраэдр(R, R, R, R, R, R).xyz_объем() self.assertAlmostEqual(tet, 0.1178511) def test_phi_edge_tetra(self): tet = Тетраэдр(D, D, D, D, D, φ ) self.assertAlmostEqual(tet.ivm_объем(), 0.70710678) def test_right_tetra(self): e = hypot(sqrt(3)/2, sqrt(3)/2) # right Тетраэдр tet = Тетраэдр(D, D, D, D, D, e).xyz_объем() self.assertAlmostEqual(tet, 1.0) def test_smod_volume(self): svol = 0.5 * φ**-5 self.assertAlmostEqual(Svol, svol) if __name__ == "__main__": unittest.main()