Platonische Körper als Graphen, sind sie plättbar?
Author: Prof. Dr. Dörte Haftendorn

Platonische Körper als Graphen

Ha 2003 und 2011

A = (-5.74064070805625, 2.2978359830495414)
B = (-3.0729692126951305, 1.331714090820522)
C = (-1.9561994522960429, 4.222128146995409)
D = (-3.7842770080446178, 5.601204197823281)
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 = (-0.32055111294205507, 4.574915043718819)
F = (2.982817101831685, 4.478700435521525)
G = (3.0148886378974495, 1.7205483338657812)
H = (-0.32055111294205507, 1.7205483338657812)
I = (1.4754549067407552, 5.953991094546691)
J = (4.554322369054144, 5.8577764863493975)
K = (4.714680049382967, 2.778909024036009)
L = (1.5075264428065196, 3.00340977649636)
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 = (-6.189642212976953, -3.699541261248414)
N = (-3.527704719518502, -0.4923876546719671)
O = (-1.0902679785204024, -1.9676783136971325)
P = (-4.104992368702263, -4.693758879287112)
Q = (-5.067138450675197, -1.8393921694340747)
R = (-2.308986349019452, -3.8278274055114716)
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 = (2.020671019858751, -0.4923876546719671)
T = (3.59217628708121, -0.7489599431980829)
U = (5.003323873974846, 0.21318613877485118)
V = (3.3035324624893296, 1.1111891486162564)
W = (0.9623103296885236, 0.886688396155905)
Z = (2.7262448133055694, -1.0055322317241986)
A_1 = (5.805112275618958, -0.7489599431980829)
B_1 = (3.9128916477388547, -1.5507483448421946)
C_1 = (1.0264534018200526, -1.8393921694340747)
D_1 = (0.06430731984711853, -0.8131030153296118)
E_1 = (1.3471687624776973, -1.2621045202503143)
F_1 = (4.586393905119908, -1.294176056316079)
G_1 = (5.965469955947781, -2.5128944268151288)
H_1 = (3.0148886378974495, -2.9298243956700665)
I_1 = (-0.12812189654746828, -2.031821385828662)
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 = (1.5716695149380486, -2.544965962880893)
m_2 = Segment(J_1, E_1)
K_1 = (4.105320864133441, -2.544965962880893)
n_2 = Segment(F_1, K_1)
L_1 = (5.195753090369434, -3.9561135497745297)
p_2 = Segment(G_1, L_1)
M_1 = (3.6242478231469746, -4.918259631747464)
q_2 = Segment(H_1, M_1)
N_1 = (0.7057380411624079, -4.661687343221348)
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 = (9.365052778918814, -4.116471230103352)
P_1 = (8.370835160880116, -0.339600757948558)
d_3 = Segment(O_1, P_1)
Q_1 = (11.304486510075508, -0.37724608746114086)
e_3 = Segment(O_1, Q_1)
R_1 = (12.053488014996208, -1.8658899120530215)
f_3 = Segment(O_1, R_1)
S_1 = (9.525410459247636, -2.063892921894426)
g_3 = Segment(O_1, S_1)
T_1 = (7.297332903499063, -1.8131030153296126)
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 = (7.569046759236004, 0.5659730354982622)
n_3 = Segment(T_1, U_1)
p_3 = Segment(P_1, U_1)
V_1 = (8.959478985471995, 2.0922621896027254)
q_3 = Segment(P_1, V_1)
r_3 = Segment(V_1, Q_1)
W_1 = (12.632772654338561, 1.8922621896027254)
s_3 = Segment(Q_1, W_1)
t_3 = Segment(R_1, W_1)
Z_1 = (13.423204880574554, -0.21510000548820488)
a_4 = Segment(R_1, Z_1)
b_4 = Segment(Z_1, S_1)
A_2 = (9.236766634655757, -0.043386149751264556)
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 = (10.615842685483628, 2.682694415838717)
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)