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

valider

valider

valider

S =

F =

A =

a: 1
b: (1 + sqrt(5)) / 2
c: (a * b)
sommets: 32
faces: 60
aretes: 90
rep1: 0
rep2: 0
rep3: 0
ChampTexte1 = Textfield(rep1)
ChampTexte2 = Textfield(rep2)
ChampTexte3 = Textfield(rep3)
d: a / b
e: (a * (2 + b))
f: ((a * 2) * b)
g: ((a * b) * b)
l1 = Sequence(Sequence[Sequence[((0 * (-1)^(i)), (d * (-1)^(j)), (e * (-1)^(k))), k, 1, 2], j, 1, 2], i, 1, 2)
l4 = Sequence(Sequence[Sequence[((d * (-1)^(j)), (e * (-1)^(k)), (0 * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l5 = Sequence(Sequence[Sequence[((e * (-1)^(j)), (0 * (-1)^(k)), (d * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l7 = Sequence(Sequence[Sequence[((d * (-1)^(j)), (c * (-1)^(k)), (f * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l8 = Sequence(Sequence[Sequence[((c * (-1)^(j)), (f * (-1)^(k)), (d * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l9 = Sequence(Sequence[Sequence[((f * (-1)^(j)), (d * (-1)^(k)), (c * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l2 = Sequence(Sequence[Sequence[((c * (-1)^(j)), (2 * (-1)^(k)), (g * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l3 = Sequence(Sequence[Sequence[((2 * (-1)^(j)), (g * (-1)^(k)), (c * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l6 = Sequence(Sequence[Sequence[((g * (-1)^(j)), (c * (-1)^(k)), (2 * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
A = Point(l7)
B = Point(l7)
C = Point(l1)
D = Point(l2)
E = Point(l3)
F = Point(l6)
G = Point(l1)
H = Point(l7)
I = Point(l7)
J = Point(l2)
K = Point(l6)
L = Point(l3)
M = Point(l9)
N = Point(l5)
O = Point(l9)
P = Point(l8)
Q = Point(l4)
R = Point(l8)
S = Point(l4)
T = Point(l8)
U = Point(l8)
V = Point(l2)
W = Point(l6)
Z = Point(l3)
A_1 = Point(l3)
B_1 = Point(l2)
C_1 = Point(l6)
D_1 = Point(l9)
E_1 = Point(l9)
F_1 = Point(l5)
G_1 = Point(l9)
H_1 = Point(l5)
I_1 = Point(l9)
J_1 = Point(l6)
K_1 = Point(l3)
L_1 = Point(l2)
M_1 = Point(l8)
N_1 = Point(l8)
O_1 = Point(l4)
P_1 = Point(l4)
Q_1 = Point(l8)
R_1 = Point(l8)
S_1 = Point(l3)
T_1 = Point(l6)
U_1 = Point(l9)
V_1 = Point(l5)
W_1 = Point(l9)
Z_1 = Point(l6)
A_2 = Point(l2)
B_2 = Point(l3)
C_2 = Point(l7)
D_2 = Point(l7)
E_2 = Point(l1)
F_2 = Point(l7)
G_2 = Point(l1)
H_2 = Point(l7)
I_2 = Point(l3)
J_2 = Point(l2)
K_2 = Point(l6)
L_2 = Point(l2)
M_2 = dual_face(C, A, B)
N_2 = dual_face(V, Z, W)
O_2 = dual_face(U, S, T)
P_2 = dual_face(Q, R, P)
Q_2 = dual_face(E, F, D)
R_2 = dual_face(D, B, A)
S_2 = dual_face(T, S, Q)
T_2 = dual_face(E, P, R)
U_2 = dual_face(Z, U, T)
V_2 = dual_face(V, A, C)
W_2 = dual_face(C, B, D)
Z_2 = dual_face(G, I, H)
A_3 = dual_face(H, I, L_1)
B_3 = dual_face(L_1, K_1, J_1)
C_3 = dual_face(J_1, I_1, H_1)
D_3 = dual_face(H_1, G_1, I_1)
E_3 = dual_face(F_1, D_1, E_1)
F_3 = dual_face(K_2, I_2, J_2)
G_3 = dual_face(N_1, O_1, P_1)
H_3 = dual_face(M_1, N_1, O_1)
I_3 = dual_face(P_1, R_1, Q_1)
J_3 = dual_face(Q_1, B_2, Z_1)
K_3 = dual_face(Z_1, B_2, A_2)
L_3 = dual_face(F_2, G_2, H_2)
M_3 = dual_face(J_2, H_2, G_2)
N_3 = dual_face(G_2, E_2, C_2)
O_3 = dual_face(O, N, M)
P_3 = dual_face(V_1, U_1, W_1)
Q_3 = dual_face(K, L, J)
R_3 = dual_face(A_1, B_1, C_1)
S_3 = dual_face(D_2, E_2, C_2)
T_3 = dual_face(L_2, T_1, S_1)
t21, o_3, g_9, h_9 = Polygon(W_2, T_2, O_3)
t22, i_9, j_9, k_9 = Polygon(W_2, O_3, J_3)
t23, l_9, m_9, n_9 = Polygon(W_2, J_3, Q_3)
t24, p_9, q_9, r_9 = Polygon(W_2, T_2, Q_2)
t25, s_9, t_9, a_9 = Polygon(O_3, T_2, J_3)
t26, b_9, c_9, d_9 = Polygon(T_2, J_3, P_3)
t27, e_9, f_{10}, g_{10} = Polygon(P_3, N_3, T_2)
t28, h_{10}, i_{10}, j_{10} = Polygon(P_3, J_3, N_3)
t29, k_{10}, l_{10}, m_{10} = Polygon(N_3, T_3, T_2)
t30, n_{10}, p_{10}, q_{10} = Polygon(N_3, K_3, J_3)
t31, r_{10}, s_{10}, t_{10} = Polygon(W_2, Q_3, A_3)
t32, a_{10}, b_{10}, c_{10} = Polygon(A_3, J_3, Q_3)
t33, d_{10}, e_{10}, f_{11} = Polygon(A_3, I_3, J_3)
t34, g_{11}, h_{11}, i_{11} = Polygon(J_3, I_3, G_3)
t35, j_{11}, k_{11}, l_{11} = Polygon(J_3, K_3, G_3)
t36, m_{11}, n_{11}, p_{11} = Polygon(A_3, G_3, I_3)
t37, q_{11}, r_{11}, s_{11} = Polygon(A_3, H_3, G_3)
t38, t_{11}, a_{11}, b_{11} = Polygon(A_3, Z_2, W_2)
t39, c_{11}, d_{11}, e_{11} = Polygon(W_2, Z_2, V_2)
t40, f_{12}, g_{12}, h_{12} = Polygon(Z_2, A_3, V_2)
t41, i_{12}, j_{12}, k_{12} = Polygon(A_3, B_3, V_2)
t42, l_{12}, m_{12}, n_{12} = Polygon(A_3, H_3, C_3)
t43, p_{12}, q_{12}, r_{12} = Polygon(A_3, B_3, C_3)
t44, s_{12}, t_{12}, a_{12} = Polygon(V_2, C_3, B_3)
t45, b_{12}, c_{12}, d_{12} = Polygon(V_2, D_3, C_3)
t46, e_{12}, f_{13}, g_{13} = Polygon(G_3, C_3, H_3)
t47, h_{13}, i_{13}, j_{13} = Polygon(W_2, M_2, V_2)
t48, k_{13}, l_{13}, m_{13} = Polygon(V_2, R_2, M_2)
t49, n_{13}, p_{13}, q_{13} = Polygon(V_2, N_2, R_2)
t50, r_{13}, s_{13}, t_{13} = Polygon(V_2, U_2, N_2)
t51, a_{13}, b_{13}, c_{13} = Polygon(V_2, D_3, U_2)
t52, d_{13}, e_{13}, f_{14} = Polygon(W_2, R_2, M_2)
t53, g_{14}, h_{14}, i_{14} = Polygon(W_2, Q_2, R_2)
t54, j_{14}, k_{14}, l_{14} = Polygon(R_2, U_2, N_2)
t55, m_{14}, n_{14}, p_{14} = Polygon(R_2, O_2, U_2)
t56, q_{14}, r_{14}, s_{14} = Polygon(R_2, S_2, O_2)
t57, t_{14}, a_{14}, b_{14} = Polygon(R_2, P_2, S_2)
t58, c_{14}, d_{14}, e_{14} = Polygon(S_2, M_3, R_3)
t59, f_{15}, g_{15}, h_{15} = Polygon(S_2, S_3, M_3)
t60, i_{15}, j_{15}, k_{15} = Polygon(U_2, R_3, S_2)
t61, l_{15}, m_{15}, n_{15} = Polygon(U_2, O_2, S_2)
t62, p_{15}, q_{15}, r_{15} = Polygon(R_2, T_2, Q_2)
t63, s_{15}, t_{15}, a_{15} = Polygon(R_2, P_2, T_2)
t64, b_{15}, c_{15}, d_{15} = Polygon(T_2, S_2, P_2)
t65, e_{15}, f_{16}, g_{16} = Polygon(T_2, T_3, S_2)
t66, h_{16}, i_{16}, j_{16} = Polygon(N_3, S_2, T_3)
t67, k_{16}, l_{16}, m_{16} = Polygon(N_3, S_3, S_2)
t68, n_{16}, p_{16}, q_{16} = Polygon(N_3, M_3, S_3)
t69, r_{16}, s_{16}, t_{16} = Polygon(N_3, L_3, M_3)
t70, a_{16}, b_{16}, c_{16} = Polygon(G_3, N_3, K_3)
t71, d_{16}, e_{16}, f_{17} = Polygon(G_3, L_3, N_3)
t72, g_{17}, h_{17}, i_{17} = Polygon(G_3, M_3, L_3)
t73, j_{17}, k_{17}, l_{17} = Polygon(G_3, F_3, M_3)
t74, m_{17}, n_{17}, p_{17} = Polygon(C_3, M_3, E_3)
t75, q_{17}, r_{17}, s_{17} = Polygon(C_3, F_3, M_3)
t76, t_{17}, a_{17}, b_{17} = Polygon(C_3, F_3, G_3)
t77, c_{17}, d_{17}, e_{17} = Polygon(C_3, U_2, D_3)
t78, f_{18}, g_{18}, h_{18} = Polygon(C_3, E_3, U_2)
t79, i_{18}, j_{18}, k_{18} = Polygon(U_2, E_3, M_3)
t80, l_{18}, m_{18}, n_{18} = Polygon(U_2, M_3, R_3)

Tool: perp_tangente_espace (command perp_tangente)
perp_tangente[ <Point>, <Point> ]
Input: L, U
Output: e_{11}

M_2 = Midpoint(L, U)
p_{12} = Plane(L, U, (0, 0, 0))
e_{11} = OrthogonalLine(M_2, p_{12})

Tool: dual_face_point (command dual_face)
dual_face[ <Point>, <Point>, <Point> ]
Input: L, U, M
Output: M_2

e_{11} = perp_tangente(L, U)
f_{12} = perp_tangente(M, U)
M_2 = Intersect(f_{12}, e_{11})