Déterminer le nombre de
sommets, de faces et
d'arêtes de ce solide.

valider

valider

valider

S =

F =

A =

r: 0.7
sommets: 60
faces: 92
aretes: 150
rep1: 0
rep2: 0
rep3: 0
ChampTexte1 = Textfield(rep1)
ChampTexte2 = Textfield(rep2)
ChampTexte3 = Textfield(rep3)
p: (1 + sqrt(5)) / 2
q: 1.7155615
s: q - 1 / q
t: (q * p) + (p * p) + p / q
a: (r * s)
b: (r * t)
c: (r * (s + t / p + p))
d: (r * ((-((s * p))) + t + 1 / p))
e: (r * (s / p + (t * p) - 1))
l4 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((c * (-1)^(i)), (d * (-1)^(j)), (e * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l6 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((d * (-1)^(i)), (e * (-1)^(j)), (c * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
f: (r * (((-s)) / p + (t * p) + 1))
g: (r * ((-s) + t / p - p))
h: (r * ((s * p) + t - 1 / p))
l7 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((f * (-1)^(i)), (g * (-1)^(j)), (h * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l8 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((h * (-1)^(i)), (f * (-1)^(j)), (g * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l: (r * (((-s)) / p + (t * p) - 1))
m: (r * (s - t / p - p))
n: (r * ((s * p) + t + 1 / p))
l10 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((l * (-1)^(i)), (m * (-1)^(j)), (n * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l11 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((n * (-1)^(i)), (l * (-1)^(j)), (m * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l12 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((m * (-1)^(i)), (n * (-1)^(j)), (l * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
u: (r * (s + t / p - p))
v: (r * ((s * p) - t + 1 / p))
w: (r * (s / p + (t * p) + 1))
l13 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((u * (-1)^(i)), (v * (-1)^(j)), (w * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l14 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((w * (-1)^(i)), (u * (-1)^(j)), (v * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l15 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((v * (-1)^(i)), (w * (-1)^(j)), (u * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l1 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, (((2 * a) * (-1)^(i)), (2 * (r * (-1)^(j))), ((2 * b) * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l2 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, (((2 * b) * (-1)^(i)), ((2 * a) * (-1)^(j)), (2 * (r * (-1)^(k))))], k, 1, 2], j, 1, 2], i, 1, 2)
l3 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((2 * (r * (-1)^(i))), ((2 * b) * (-1)^(j)), ((2 * a) * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l9 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((g * (-1)^(i)), (h * (-1)^(j)), (f * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l5 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((e * (-1)^(i)), (c * (-1)^(j)), (d * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
A = Point(l1)
B = Point(l1)
C = Point(l13)
t1, c_1, a_1, b_1 = Polygon(A, B, C)
D = Point(l9)
t2, a_2, c_2, d_1 = Polygon(C, D, A)
E = Point(l4)
t3, d_2, a_3, e_1 = Polygon(A, E, D)
F = Point(l7)
G = Point(l10)
H = Point(l13)
poly1, a_4, e_2, f_1, g_1, h_1 = Polygon(A, E, F, G, H)
t4, b_2, a_5, h_2 = Polygon(A, H, B)
I = Point(l9)
t5, i, h_3, b_3 = Polygon(H, B, I)
J = Point(l12)
t6, i_1, h_4, j = Polygon(H, J, I)
t7, j_1, h_5, g_2 = Polygon(H, G, J)
K = Point(l11)
t8, k, g_3, j_2 = Polygon(G, J, K)
L = Point(l14)
t9, l_1, g_4, k_1 = Polygon(G, K, L)
t10, f_2, g_5, l_2 = Polygon(G, L, F)
M = Point(l2)
t11, l_3, f_3, m_1 = Polygon(F, M, L)
N = Point(l5)
t12, m_2, f_4, n_1 = Polygon(F, N, M)
t13, n_2, f_5, e_3 = Polygon(F, E, N)
O = Point(l6)
t14, n_3, e_4, o = Polygon(E, O, N)
t15, d_3, e_5, o_1 = Polygon(E, O, D)
P = Point(l12)
Q = Point(l15)
R = Point(l3)
poly2, d_4, p_1, q_1, r_1, o_2 = Polygon(D, P, Q, R, O)
S = Point(l8)
t16, r_2, o_3, s_1 = Polygon(O, S, R)
t17, o_4, n_4, s_2 = Polygon(N, S, O)
T = Point(l15)
t18, r_3, s_3, t_1 = Polygon(S, T, R)
U = Point(l3)
t19, t_2, r_4, u_1 = Polygon(R, U, T)
t20, q_2, r_5, u_2 = Polygon(R, U, Q)
V = Point(l8)
t21, u_3, q_3, v_1 = Polygon(Q, V, U)
W = Point(l11)
t22, v_2, q_4, w_1 = Polygon(Q, W, V)
t23, w_2, q_5, p_2 = Polygon(Q, P, W)
t24, p_3, d_5, c_3 = Polygon(D, C, P)
Z = Point(l10)
t25, p_4, z_1, w_3 = Polygon(Z, W, P)
t26, p_5, c_4, z_2 = Polygon(C, Z, P)
A_1 = Point(l7)
B_1 = Point(l4)
poly3, c_5, z_3, i_2, k_2, b_4 = Polygon(C, Z, A_1, B_1, B)
t27, b_5, i_3, j_3 = Polygon(I, B_1, B)
C_1 = Point(l6)
t28, i_4, k_3, m_3 = Polygon(B_1, C_1, I)
D_1 = Point(l15)
E_1 = Point(l3)
poly4, t_3, j_4, k_4, i_5, j_5 = Polygon(D_1, E_1, C_1, I, J)
F_1 = Point(l5)
t29, l_4, m_4, s_4 = Polygon(B_1, F_1, C_1)
G_1 = Point(l8)
t30, t_4, k_5, l_5 = Polygon(C_1, G_1, F_1)
t31, m_5, n_5, s_5 = Polygon(E_1, G_1, C_1)
H_1 = Point(l15)
t32, t_5, f_6, g_6 = Polygon(G_1, H_1, E_1)
I_1 = Point(l3)
t33, h_6, i_6, j_6 = Polygon(E_1, I_1, H_1)
t34, k_6, l_6, m_6 = Polygon(D_1, I_1, E_1)
t35, n_6, j_7, k_7 = Polygon(J, K, D_1)
J_1 = Point(l8)
t36, p_6, k_8, q_6 = Polygon(K, J_1, D_1)
t37, r_6, s_6, t_6 = Polygon(J_1, I_1, D_1)
K_1 = Point(l5)
L_1 = Point(l2)
poly5, k_9, a_6, b_6, c_6, l_7 = Polygon(K, J_1, K_1, L_1, L)
t38, l_8, m_7, d_6 = Polygon(M, L_1, L)
M_1 = Point(l6)
t39, e_6, f_7, g_7 = Polygon(J_1, M_1, K_1)
t40, h_7, i_7, n_7 = Polygon(M_1, I_1, J_1)
N_1 = Point(l9)
O_1 = Point(l12)
poly6, p_7, q_7, r_7, s_7, t_7 = Polygon(I_1, M_1, N_1, O_1, H_1)
P_1 = Point(l11)
t41, a_7, b_7, c_7 = Polygon(H_1, O_1, P_1)
t42, d_7, e_7, f_8 = Polygon(H_1, G_1, P_1)
Q_1 = Point(l2)
R_1 = Point(l14)
poly7, g_8, h_8, i_8, j_8, m_8 = Polygon(F_1, Q_1, R_1, P_1, G_1)
t43, n_8, p_8, q_8 = Polygon(B_1, F_1, A_1)
t44, r_8, s_8, t_8 = Polygon(F_1, A_1, Q_1)
S_1 = Point(l14)
t45, a_8, b_8, c_8 = Polygon(A_1, S_1, Q_1)
t46, z_4, d_8, e_8 = Polygon(A_1, S_1, Z)
t47, z_5, f_9, w_4 = Polygon(S_1, W, Z)
T_1 = Point(l2)
t48, g_9, h_9, i_9 = Polygon(S_1, T_1, Q_1)
t49, j_9, l_9, m_9 = Polygon(T_1, R_1, Q_1)
U_1 = Point(l5)
poly8, n_9, p_9, q_9, v_3, w_5 = Polygon(S_1, T_1, U_1, V, W)
V_1 = Point(l7)
t50, r_9, s_9, t_9 = Polygon(R_1, V_1, T_1)
t51, a_9, b_9, c_9 = Polygon(T_1, V_1, U_1)
W_1 = Point(l10)
t52, d_9, e_9, f_{10} = Polygon(O_1, W_1, P_1)
t53, g_{10}, h_{10}, i_{10} = Polygon(R_1, W_1, P_1)
t54, j_{10}, k_{10}, l_{10} = Polygon(W_1, V_1, R_1)
Z_1 = Point(l6)
t55, m_{10}, v_4, n_{10} = Polygon(V, U_1, Z_1)
t56, v_5, p_{10}, u_4 = Polygon(Z_1, U, V)
A_2 = Point(l9)
B_2 = Point(l12)
poly9, q_{10}, r_{10}, s_{10}, t_{10}, u_5 = Polygon(Z_1, A_2, B_2, T, U)
C_2 = Point(l11)
D_2 = Point(l14)
poly10, n_{11}, s_{11}, a_{10}, b_{10}, m_{11} = Polygon(N, S, C_2, D_2, M)
t57, c_{10}, s_{12}, t_{11} = Polygon(S, T, C_2)
t58, d_{10}, t_{12}, e_{10} = Polygon(T, B_2, C_2)
t59, f_{11}, m_{12}, g_{11} = Polygon(M, D_2, L_1)
E_2 = Point(l7)
t60, h_{11}, i_{11}, j_{11} = Polygon(L_1, E_2, K_1)
t61, k_{11}, l_{11}, p_{11} = Polygon(L_1, E_2, D_2)
F_2 = Point(l10)
t62, q_{11}, r_{11}, a_{11} = Polygon(C_2, B_2, F_2)
t63, b_{11}, c_{11}, d_{11} = Polygon(C_2, F_2, D_2)
t64, e_{11}, f_{12}, g_{12} = Polygon(F_2, E_2, D_2)
G_2 = Point(l13)
t65, h_{12}, i_{12}, j_{12} = Polygon(B_2, G_2, F_2)
H_2 = Point(l1)
I_2 = Point(l4)
poly11, k_{12}, l_{12}, n_{12}, p_{12}, q_{12} = Polygon(F_2, G_2, H_2, I_2, E_2)
t66, r_{12}, a_{12}, b_{12} = Polygon(K_1, I_2, E_2)
t67, c_{12}, d_{12}, e_{12} = Polygon(K_1, I_2, M_1)
t68, f_{13}, g_{13}, h_{13} = Polygon(I_2, N_1, M_1)
t69, i_{13}, j_{13}, k_{13} = Polygon(I_2, H_2, N_1)
J_2 = Point(l13)
t70, l_{13}, m_{13}, n_{13} = Polygon(N_1, J_2, O_1)
t71, p_{13}, q_{13}, r_{13} = Polygon(N_1, H_2, J_2)
t72, s_{13}, t_{13}, a_{13} = Polygon(W_1, J_2, O_1)
K_2 = Point(l4)
L_2 = Point(l1)
poly12, b_{13}, c_{13}, d_{13}, e_{13}, f_{14} = Polygon(V_1, K_2, L_2, J_2, W_1)
t73, g_{14}, h_{14}, i_{14} = Polygon(U_1, K_2, V_1)
t74, j_{14}, k_{14}, l_{14} = Polygon(K_2, Z_1, U_1)
t75, m_{14}, n_{14}, p_{14} = Polygon(K_2, A_2, Z_1)
t76, q_{14}, r_{14}, s_{14} = Polygon(A_2, L_2, K_2)
t77, t_{14}, a_{14}, b_{14} = Polygon(A_2, G_2, B_2)
t78, c_{14}, d_{14}, e_{14} = Polygon(A_2, L_2, G_2)
t79, f_{15}, g_{15}, h_{15} = Polygon(L_2, H_2, G_2)
t80, i_{15}, j_{15}, k_{15} = Polygon(L_2, H_2, J_2)