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

valider

valider

valider

S =

F =

A =

a: 2
b: (1 + sqrt(5)) / 2
c: (a * b)
sommets: 32
faces: 30
aretes: 60
rep1: 0
rep2: 0
rep3: 0
ChampTexte1 = Textfield(rep1)
ChampTexte2 = Textfield(rep2)
ChampTexte3 = Textfield(rep3)
d: (a * b / 2)
e: (a * (1 + b) / 2)
l1 = Sequence(Sequence[Sequence[((0 * (-1)^(i)), (0 * (-1)^(j)), (c * (-1)^(k))), k, 1, 2], j, 1, 2], i, 1, 2)
l4 = Sequence(Sequence[Sequence[((c * (-1)^(j)), (0 * (-1)^(k)), (0 * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l5 = Sequence(Sequence[Sequence[((0 * (-1)^(j)), (c * (-1)^(k)), (0 * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l7 = Sequence(Sequence[Sequence[((0.5 * (a * (-1)^(j))), (d * (-1)^(k)), (e * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l8 = Sequence(Sequence[Sequence[((e * (-1)^(j)), (0.5 * (a * (-1)^(k))), (d * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l9 = Sequence(Sequence[Sequence[((d * (-1)^(j)), (e * (-1)^(k)), (0.5 * (a * (-1)^(i)))), k, 1, 2], j, 1, 2], i, 1, 2)
A = Point(l7)
B = Point(l7)
C = Point(l1)
G = Point(l1)
H = Point(l7)
I = Point(l7)
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)
D_1 = Point(l9)
E_1 = Point(l9)
F_1 = Point(l5)
G_1 = Point(l9)
H_1 = Point(l5)
I_1 = Point(l9)
M_1 = Point(l8)
N_1 = Point(l8)
O_1 = Point(l4)
P_1 = Point(l4)
Q_1 = Point(l8)
R_1 = Point(l8)
U_1 = Point(l9)
V_1 = Point(l5)
W_1 = Point(l9)
C_2 = Point(l7)
D_2 = Point(l7)
E_2 = Point(l1)
F_2 = Point(l7)
G_2 = Point(l1)
H_2 = Point(l7)
D = Point(l5)
A_1: (0, 0, 0)
E = point_dual(B, M, P, A_1)
F = point_dual(G, B, P, A_1)
J = point_dual(G, B, A, A_1)
K = point_dual(A, G_1, V_1, A_1)
q1, f, j_6, k_6, e_5 = Polygon(F, J, K, E)
L = point_dual(G, I, M_1, A_1)
V = point_dual(U, O_1, T, A_1)
W = point_dual(M_1, O_1, U, A_1)
Z = point_dual(I_1, M_1, O_1, A_1)
B_1 = point_dual(O_1, N_1, T, A_1)
C_1 = point_dual(A, G_1, U, A_1)
J_1 = point_dual(G_1, D_1, V_1, A_1)
K_1 = point_dual(D_1, T, D_2, A_1)
L_1 = point_dual(V_1, D_1, D_2, A_1)
S_1 = point_dual(M, V_1, U_1, A_1)
T_1 = point_dual(U_1, C_2, R, A_1)
Z_1 = point_dual(P, M, U_1, A_1)
A_2 = point_dual(P_1, R, Q_1, A_1)
B_2 = point_dual(P, P_1, R_1, A_1)
I_2 = point_dual(R, C_2, G_2, A_1)
J_2 = point_dual(Q_1, F_2, W_1, A_1)
K_2 = point_dual(F_2, G_2, H_2, A_1)
L_2 = point_dual(G, H, I, A_1)
M_2 = point_dual(H, O, R_1, A_1)
N_2 = point_dual(O, W_1, D, A_1)
O_2 = point_dual(I_1, D, E_1, A_1)
P_2 = point_dual(I, I_1, M_1, A_1)
Q_2 = point_dual(E_1, H_2, N_1, A_1)
R_2 = point_dual(D_2, G_2, C_2, A_1)
S_2 = point_dual(I, I_1, D, A_1)
T_2 = point_dual(D, W_1, F_2, A_1)
U_2 = point_dual(R_1, P_1, Q_1, A_1)
V_2 = point_dual(T, N_1, H_2, A_1)
q2, k_7, j_7, l_6, f_6 = Polygon(K, J, L, C_1)
q3, k_8, g_6, v, h_6 = Polygon(K, C_1, V, J_1)
q4, k_9, i_6, m_6, n_6 = Polygon(K, J_1, L_1, S_1)
q5, k_{10}, p_6, z_1, e_6 = Polygon(K, S_1, Z_1, E)
q6, l_7, j_8, f_7, q_6 = Polygon(L, J, F, L_2)
q7, s_6, a_6, f_8, b_6 = Polygon(S_2, L_2, F, M_2)
q8, f_9, c_6, d_6, g_7 = Polygon(F, M_2, U_2, B_2)
q9, f_{10}, h_7, i_7, e_7 = Polygon(F, B_2, Z_1, E)
q10, l_8, m_7, n_7, p_7 = Polygon(L, L_2, S_2, P_2)
q11, l_9, q_7, z_2, w = Polygon(L, P_2, Z, W)
q12, l_{10}, w_2, v_2, r_7 = Polygon(L, W, V, C_1)
q13, z_3, s_7, v_3, w_3 = Polygon(Z, B_1, V, W)
q14, z_4, t_7, a_7, b_7 = Polygon(Z, B_1, V_2, Q_2)
q15, z_5, c_7, d_7, g_8 = Polygon(Z, Q_2, T_2, O_2)
q16, z_6, h_8, i_8, m_8 = Polygon(Z, O_2, S_2, P_2)
q17, n_8, p_8, q_8, r_8 = Polygon(S_2, O_2, T_2, N_2)
q18, s_8, t_8, a_8, b_8 = Polygon(S_2, N_2, U_2, M_2)
q19, c_8, d_8, e_8, g_9 = Polygon(U_2, J_2, T_2, N_2)
q20, h_9, i_9, j_9, m_9 = Polygon(U_2, J_2, I_2, A_2)
q21, n_9, p_9, q_9, r_9 = Polygon(U_2, A_2, Z_1, B_2)
q22, s_9, t_9, a_9, b_9 = Polygon(Z_1, T_1, I_2, A_2)
q26, m, t_1, n, s_1 = Polygon(Z_1, T_1, L_1, S_1)
q27, i_2, p, q, r = Polygon(I_2, R_2, L_1, T_1)
q23, v_1, k_1, g, b_1 = Polygon(V, K_1, V_2, B_1)
q24, v_4, h, l_1, j_1 = Polygon(V, K_1, L_1, J_1)
q25, i, j, k, r_2 = Polygon(L_1, K_1, V_2, R_2)
q28, t_2, k_2, l, j_2 = Polygon(T_2, K_2, I_2, J_2)
q29, s, t, f_1, q_2 = Polygon(T_2, K_2, V_2, Q_2)
q30, g_1, h_1, i_1, m_1 = Polygon(K_2, I_2, R_2, V_2)

Tool: perp_espace
Outil1[ <Point>, <Point>, <Point> ]
Input: W, H, A1
Output: f_5

A1: (0, 0, 0)
A_1 = Midpoint(W, H)
p_5 = Plane(W, H, A1)
f_5 = OrthogonalLine(A_1, p_5)

Tool: point_dual
point_dual[ <Point>, <Point>, <Point>, <Point> ]
Input: B, C, D, O
Output: M

O: (0, 0, 0)
m = perp_espace(B, C, O)
n = perp_espace(C, D, O)
M = Intersect(n, m)