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

valider

valider

valider

S =

F =

A =

a: 1.6
d: ((1 + (2 * sqrt(2))) * a / 2)
c: ((1 + sqrt(2)) * a / 2)
b: a / 2
sommets: 26
faces: 48
aretes: 72
rep1: 0
rep2: 0
rep3: 0
ChampTexte1 = Textfield(rep1)
ChampTexte2 = Textfield(rep2)
ChampTexte3 = Textfield(rep3)
l2 = Sequence(Sequence[Sequence[((b * (-1)^(k)), (d * (-1)^(j)), (c * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l3 = Sequence(Sequence[Sequence[((c * (-1)^(j)), (b * (-1)^(k)), (d * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l1 = Sequence(Sequence[Sequence[((b * (-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(l1)
D = Point(l1)
Q = Point(l3)
R = Point(l3)
S = Point(l3)
T = Point(l3)
W = Point(l2)
A_1 = Point(l2)
B_1 = Point(l2)
E_1 = Point(l2)
I_1 = Point(l2)
K_1 = Point(l2)
L_1 = Point(l2)
O_1 = Point(l2)
Q_1 = Point(l3)
S_1 = Point(l3)
A_2 = Point(l3)
C_2 = Point(l3)
F_2 = Point(l1)
J_2 = Point(l1)
K_2 = Point(l1)
L_2 = Point(l1)
l4 = Sequence(Sequence[Sequence[((c * (-1)^(j)), (d * (-1)^(k)), (b * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l5 = Sequence(Sequence[Sequence[((d * (-1)^(j)), (b * (-1)^(k)), (c * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l6 = Sequence(Sequence[Sequence[((d * (-1)^(j)), (c * (-1)^(k)), (b * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
E = Point(l5)
F = Point(l6)
G = Point(l4)
H = Point(l4)
I = Point(l6)
J = Point(l5)
K = Point(l5)
L = Point(l6)
M = Point(l4)
N = Point(l4)
O = Point(l6)
P = Point(l5)
U = Point(l6)
V = Point(l5)
Z = Point(l5)
C_1 = Point(l6)
D_1 = Point(l4)
F_1 = Point(l4)
G_1 = Point(l6)
H_1 = Point(l5)
J_1 = Point(l6)
M_1 = Point(l5)
N_1 = Point(l4)
P_1 = Point(l4)
R_1 = dual_face(T, J, K)
T_1 = dual_face(K, L, M)
U_1 = dual_face(M, N_1, J_1)
V_1 = dual_face(J_1, L, K)
W_1 = dual_face(J, T, D)
Z_1 = dual_face(T, Q, A)
B_2 = dual_face(A, B_1, I_1)
D_2 = dual_face(I_1, B_1, M)
E_2 = dual_face(N_1, J_1, M_1)
G_2 = dual_face(M_1, H_1, S_1)
H_2 = dual_face(H_1, G_1, F_1)
I_2 = dual_face(F_1, H, I)
M_2 = dual_face(W, H, F_1)
N_2 = dual_face(A_1, L_2, J_2)
O_2 = dual_face(W, L_1, C)
P_2 = dual_face(C_1, D_1, G)
Q_2 = dual_face(O_1, J_2, Q_1)
R_2 = dual_face(Q_1, C_2, K_2)
S_2 = dual_face(V, Z, Q_1)
T_2 = dual_face(Z, C_1, F)
U_2 = dual_face(S, E, F)
V_2 = dual_face(E, S, R)
W_2 = dual_face(B, I_1, N)
Z_2 = dual_face(N, P_1, U)
A_3 = dual_face(V, U, P_1)
B_3 = dual_face(K_2, K_1, E_1)
t1, f_7, g_7, h_7 = Polygon(Z_1, O_2, W_1)
t3, k_7, l_7, m_7 = Polygon(Z_1, W_1, R_1)
t4, n_7, p_7, q_7 = Polygon(Z_1, R_1, T_1)
t5, r_7, s_7, t_7 = Polygon(Z_1, T_1, B_2)
t6, a_7, b_7, c_7 = Polygon(Z_1, W_2, B_2)
t7, d_7, f_8, g_8 = Polygon(Z_1, W_2, V_2)
t2, i_7, j_7, e_7 = Polygon(Z_1, V_2, U_2)
t8, h_8, i_8, j_8 = Polygon(Z_1, U_2, O_2)
t9, k_8, l_8, m_8 = Polygon(T_2, V_2, W_2)
t10, n_8, p_8, q_8 = Polygon(T_2, W_2, Z_2)
t11, r_8, s_8, t_8 = Polygon(T_2, Z_2, A_3)
t12, a_8, b_8, c_8 = Polygon(T_2, A_3, S_2)
t13, d_8, e_8, f_9 = Polygon(T_2, S_2, Q_2)
t14, g_9, h_9, i_9 = Polygon(T_2, Q_2, P_2)
t15, j_9, k_9, l_9 = Polygon(T_2, P_2, U_2)
t16, m_9, n_9, p_9 = Polygon(T_2, U_2, V_2)
t17, q_9, r_9, s_9 = Polygon(D_2, B_2, T_1)
t18, t_9, a_9, b_9 = Polygon(D_2, T_1, U_1)
t19, c_9, d_9, e_9 = Polygon(D_2, U_1, E_2)
t20, f_{10}, g_{10}, h_{10} = Polygon(D_2, E_2, B_3)
t21, i_{10}, j_{10}, k_{10} = Polygon(D_2, B_3, A_3)
t22, l_{10}, m_{10}, n_{10} = Polygon(D_2, A_3, Z_2)
t23, p_{10}, q_{10}, r_{10} = Polygon(D_2, Z_2, W_2)
t24, s_{10}, t_{10}, a_{10} = Polygon(D_2, W_2, B_2)
t25, b_{10}, c_{10}, d_{10} = Polygon(R_1, V_1, T_1)
t26, e_{10}, f_{11}, g_{11} = Polygon(R_1, W_1, V_1)
t27, h_{11}, i_{11}, j_{11} = Polygon(V_1, W_1, I_2)
t28, k_{11}, l_{11}, m_{11} = Polygon(V_1, I_2, H_2)
t29, n_{11}, p_{11}, q_{11} = Polygon(V_1, H_2, G_2)
t30, r_{11}, s_{11}, t_{11} = Polygon(V_1, G_2, E_2)
t31, a_{11}, b_{11}, c_{11} = Polygon(V_1, E_2, U_1)
t32, d_{11}, e_{11}, f_{12} = Polygon(V_1, U_1, T_1)
t33, g_{12}, h_{12}, i_{12} = Polygon(M_2, O_2, U_2)
t34, j_{12}, k_{12}, l_{12} = Polygon(M_2, U_2, P_2)
t35, m_{12}, n_{12}, p_{12} = Polygon(M_2, P_2, Q_2)
t36, q_{12}, r_{12}, s_{12} = Polygon(M_2, Q_2, N_2)
t37, t_{12}, a_{12}, b_{12} = Polygon(M_2, N_2, H_2)
t38, c_{12}, d_{12}, e_{12} = Polygon(M_2, H_2, I_2)
t39, f_{13}, g_{13}, h_{13} = Polygon(M_2, I_2, W_1)
t40, i_{13}, j_{13}, k_{13} = Polygon(M_2, W_1, O_2)
t41, l_{13}, m_{13}, n_{13} = Polygon(R_2, N_2, Q_2)
t42, p_{13}, q_{13}, r_{13} = Polygon(R_2, Q_2, S_2)
t43, s_{13}, t_{13}, a_{13} = Polygon(R_2, S_2, A_3)
t44, b_{13}, c_{13}, d_{13} = Polygon(R_2, A_3, B_3)
t45, e_{13}, f_{14}, g_{14} = Polygon(R_2, B_3, E_2)
t46, h_{14}, i_{14}, j_{14} = Polygon(R_2, E_2, G_2)
t47, k_{14}, l_{14}, m_{14} = Polygon(R_2, G_2, H_2)
t48, n_{14}, p_{14}, q_{14} = Polygon(R_2, H_2, N_2)

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})