Platonische Graphen sind planar
Author: Prof. Dr. Dörte Haftendorn

www.mathematik-verstehen.de   Bereich Graphentheorie

Platonische Körper als planare Graphen

Ha 2003 und 2011

A = (-4.611607781800608, 1.6736337728439614)
B = (-0.9644645068839215, 2.1105311443183563)
C = (-3.1299558263657037, 4.65593322160396)
D = (-2.88301383379322, 2.832361584145617)
a = Segment(A, B)
b = Segment(B, C)
c = Segment(C, A)
d = Segment(D, B)
e = Segment(D, C)
f = Segment(D, A)
E = (2.6446876922523823, 3.5351964860826866)
F = (3.993370882455949, 3.5351964860826866)
G = (3.993370882455949, 2.4524508263417952)
H = (2.6066966164720005, 2.4524508263417952)
I = (1.5809375704016824, 4.503968918482431)
J = (5.26607192109875, 4.4849733805922405)
K = (5.304062996879133, 1.1987453255891847)
L = (1.485959880950727, 1.255731939259758)
g = Segment(I, J)
h = Segment(J, K)
i = Segment(K, L)
j = Segment(L, I)
k = Segment(E, F)
l = Segment(F, G)
m = Segment(G, H)
n = Segment(H, E)
p = Segment(E, I)
q = Segment(F, J)
r = Segment(G, K)
s = Segment(H, L)
M = (-4.231697023996786, -2.9802730102528514)
N = (-3.3579022810479966, -2.6763444040097943)
O = (-1.405022310549045, -4.037991075780383)
P = (-5.086496229055385, -5.012795564503296)
Q = (-4.592612243910416, -0.510853084528012)
R = (-3.5858487357302895, -3.7021034500801124)
t = Segment(M, N)
a_1 = Segment(N, O)
b_1 = Segment(O, P)
c_1 = Segment(P, M)
d_1 = Segment(Q, M)
e_1 = Segment(Q, N)
f_1 = Segment(Q, P)
g_1 = Segment(Q, O)
h_1 = Segment(R, N)
i_1 = Segment(R, O)
j_1 = Segment(R, M)
k_1 = Segment(R, P)
S = (1.4289732672801538, -2.999268548143043)
T = (2.4547323133504717, -3.1702283891547625)
U = (2.9866073742758217, -2.2014559567550176)
V = (2.188794782887797, -1.3276612138062283)
W = (1.2770089641586253, -1.9735095020727247)
Z = (2.188794782887797, -0.8907638423318335)
A_1 = (3.48049135942079, -1.8785318126217694)
B_1 = (2.7586609195935288, -3.6210989879703033)
C_1 = (0.9501562137823197, -3.507125760629157)
D_1 = (0.6311606758921287, -1.764558585280623)
E_1 = (0.8591071305744216, -0.4728620087476299)
F_1 = (3.7274333519932736, -0.776790614990687)
G_1 = (4.0693530340167126, -3.0182640860332337)
H_1 = (1.6759152598526377, -4.480920503577947)
I_1 = (-0.22363852916646962, -2.7333310176803676)
l_1 = Segment(W, V)
m_1 = Segment(V, U)
n_1 = Segment(U, T)
p_1 = Segment(T, S)
q_1 = Segment(S, W)
r_1 = Segment(U, A_1)
s_1 = Segment(V, Z)
t_1 = Segment(W, D_1)
a_2 = Segment(S, C_1)
b_2 = Segment(T, B_1)
c_2 = Segment(G_1, B_1)
d_2 = Segment(B_1, H_1)
e_2 = Segment(C_1, H_1)
f_2 = Segment(C_1, I_1)
g_2 = Segment(I_1, D_1)
h_2 = Segment(D_1, E_1)
i_2 = Segment(E_1, Z)
j_2 = Segment(Z, F_1)
k_2 = Segment(F_1, A_1)
l_2 = Segment(A_1, G_1)
J_1 = (0.194263304417734, 0.4199282720913506)
m_2 = Segment(J_1, E_1)
K_1 = (4.639219170722445, -0.016969099383044115)
n_2 = Segment(F_1, K_1)
L_1 = (5, -3.5)
p_2 = Segment(G_1, L_1)
M_1 = (1.6569197219624467, -5.354715246526736)
q_2 = Segment(H_1, M_1)
N_1 = (-1.0594421963348768, -3.151232851264571)
r_2 = Segment(I_1, N_1)
s_2 = Segment(J_1, N_1)
t_2 = Segment(N_1, M_1)
a_3 = Segment(M_1, L_1)
b_3 = Segment(L_1, K_1)
c_3 = Segment(J_1, K_1)
O_1 = (8.153393680407794, -1.289670138025846)
P_1 = (8.191384756188176, -0.3778843192966745)
d_3 = Segment(O_1, P_1)
Q_1 = (8.894219658125246, -0.9667459938925977)
e_3 = Segment(O_1, Q_1)
R_1 = (8.761250892893909, -2.011500577853107)
f_3 = Segment(O_1, R_1)
S_1 = (7.5, -2)
g_3 = Segment(O_1, S_1)
T_1 = (7.412567702690342, -1.00473706967298)
h_3 = Segment(O_1, T_1)
i_3 = Segment(T_1, P_1)
j_3 = Segment(P_1, Q_1)
k_3 = Segment(R_1, Q_1)
l_3 = Segment(R_1, S_1)
m_3 = Segment(S_1, T_1)
U_1 = (7.355581089019768, 0.21097735529924877)
n_3 = Segment(T_1, U_1)
p_3 = Segment(P_1, U_1)
V_1 = (9.388103643270213, 0.28695950686001304)
q_3 = Segment(P_1, V_1)
r_3 = Segment(V_1, Q_1)
W_1 = (9.36910810538002, -1.992505039962916)
s_3 = Segment(Q_1, W_1)
t_3 = Segment(R_1, W_1)
Z_1 = (9.217143802258494, -4.974804488722914)
a_4 = Segment(R_1, Z_1)
b_4 = Segment(Z_1, S_1)
A_2 = (5.057121004306649, 0.21097735529924877)
c_4 = Segment(A_2, S_1)
d_4 = Segment(A_2, T_1)
e_4 = Segment(A_2, U_1)
f_4 = Segment(U_1, V_1)
g_4 = Segment(V_1, W_1)
h_4 = Segment(W_1, Z_1)
j_4 = Segment(A_2, Z_1)
B_2 = (10.660804681913014, 1.4456873181616685)
k_4 = Segment(A_2, B_2)
l_4 = Segment(B_2, U_1)
m_4 = Segment(B_2, V_1)
n_4 = Segment(B_2, W_1)
p_4 = Segment(B_2, Z_1)