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

valider

valider

valider

S =

F =

A =

a: 0.8
b: (1 + sqrt(5)) / 2
c: (a * b)
sommets: 62
faces: 120
aretes: 180
rep1: 0
rep2: 0
rep3: 0
ChampTexte1 = Textfield(rep1)
ChampTexte2 = Textfield(rep2)
ChampTexte3 = Textfield(rep3)
d: a / b
e: (a * (3 + b))
f: (a * 2 / b)
g: (a * ((2 * b) + 1))
h: ((a * b) * b)
m: (a * ((3 * b) - 1))
n: (a * ((2 * b) - 1))
r: (a * (2 + b))
s: ((a * 2) * b)
l1 = Sequence(Sequence[Sequence[((d * (-1)^(i)), (d * (-1)^(j)), (e * (-1)^(k))), k, 1, 2], j, 1, 2], i, 1, 2)
l4 = Sequence(Sequence[Sequence[((e * (-1)^(j)), (d * (-1)^(k)), (d * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l5 = Sequence(Sequence[Sequence[((d * (-1)^(j)), (e * (-1)^(k)), (d * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l7 = Sequence(Sequence[Sequence[((f * (-1)^(j)), (c * (-1)^(k)), (g * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l8 = Sequence(Sequence[Sequence[((g * (-1)^(j)), (f * (-1)^(k)), (c * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l9 = Sequence(Sequence[Sequence[((c * (-1)^(j)), (g * (-1)^(k)), (f * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l2 = Sequence(Sequence[Sequence[((d * (-1)^(j)), (h * (-1)^(k)), (m * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l3 = Sequence(Sequence[Sequence[((m * (-1)^(j)), (d * (-1)^(k)), (h * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l6 = Sequence(Sequence[Sequence[((h * (-1)^(j)), (m * (-1)^(k)), (d * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l13 = Sequence(Sequence[Sequence[((c * (-1)^(j)), (3 * (a * (-1)^(k))), (s * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l14 = Sequence(Sequence[Sequence[((3 * (a * (-1)^(j))), (s * (-1)^(k)), (c * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l15 = Sequence(Sequence[Sequence[((s * (-1)^(j)), (c * (-1)^(k)), (3 * (a * (-1)^(i)))), k, 1, 2], j, 1, 2], i, 1, 2)
A = Point(l1)
B = Point(l1)
C = Point(l1)
D = Point(l1)
E = Point(l1)
F = Point(l1)
G = Point(l1)
H = Point(l1)
I = Point(l4)
J = Point(l4)
K = Point(l4)
L = Point(l4)
M = Point(l4)
N = Point(l4)
O = Point(l4)
P = Point(l4)
Q = Point(l5)
R = Point(l5)
S = Point(l5)
T = Point(l5)
U = Point(l5)
V = Point(l5)
W = Point(l5)
Z = Point(l5)
A_1 = Point(l7)
B_1 = Point(l2)
C_1 = Point(l2)
D_1 = Point(l7)
l10 = Sequence(Sequence[Sequence[((n * (-1)^(j)), (2 * (a * (-1)^(k))), (r * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l11 = Sequence(Sequence[Sequence[((r * (-1)^(j)), (n * (-1)^(k)), (2 * (a * (-1)^(i)))), k, 1, 2], j, 1, 2], i, 1, 2)
l12 = Sequence(Sequence[Sequence[((2 * (a * (-1)^(j))), (r * (-1)^(k)), (n * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
E_1 = Point(l13)
F_1 = Point(l10)
G_1 = Point(l13)
H_1 = Point(l10)
I_1 = Point(l12)
J_1 = Point(l9)
K_1 = Point(l9)
L_1 = Point(l12)
M_1 = Point(l14)
N_1 = Point(l11)
O_1 = Point(l15)
P_1 = Point(l6)
Q_1 = Point(l3)
R_1 = Point(l3)
S_1 = Point(l15)
T_1 = Point(l10)
U_1 = Point(l7)
V_1 = Point(l2)
W_1 = Point(l2)
Z_1 = Point(l7)
A_2 = Point(l13)
B_2 = Point(l10)
C_2 = Point(l15)
D_2 = Point(l3)
E_2 = Point(l3)
F_2 = Point(l15)
G_2 = Point(l11)
H_2 = Point(l14)
I_2 = Point(l8)
J_2 = Point(l8)
K_2 = Point(l11)
L_2 = Point(l6)
M_2 = Point(l6)
N_2 = Point(l9)
O_2 = Point(l9)
P_2 = Point(l6)
Q_2 = Point(l8)
R_2 = Point(l14)
S_2 = Point(l11)
T_2 = Point(l8)
U_2 = Point(l8)
V_2 = Point(l11)
W_2 = Point(l14)
Z_2 = Point(l12)
A_3 = Point(l13)
B_3 = Point(l9)
C_3 = Point(l9)
D_3 = Point(l12)
E_3 = Point(l14)
F_3 = Point(l6)
G_3 = Point(l8)
H_3 = Point(l11)
I_3 = Point(l14)
J_3 = Point(l12)
K_3 = Point(l12)
L_3 = Point(l13)
M_3 = Point(l2)
N_3 = Point(l7)
O_3 = Point(l10)
P_3 = Point(l15)
Q_3 = Point(l3)
R_3 = Point(l6)
S_3 = Point(l8)
T_3 = Point(l11)
U_3 = Point(l14)
V_3 = Point(l6)
W_3 = Point(l9)
Z_3 = Point(l12)
A_4 = Point(l9)
B_4 = Point(l6)
C_4 = Point(l14)
D_4 = Point(l11)
E_4 = Point(l8)
F_4 = Point(l12)
G_4 = Point(l15)
H_4 = Point(l3)
I_4 = Point(l13)
J_4 = Point(l10)
K_4 = Point(l3)
L_4 = Point(l15)
M_4 = Point(l10)
N_4 = Point(l13)
O_4 = Point(l2)
P_4 = Point(l7)
Q_4 = Point(l7)
R_4 = Point(l2)
S_4 = Point(l15)
T_4 = Point(l10)
U_4 = Point(l13)
V_4 = Point(l3)
W_4 = Point(l7)
Z_4 = Point(l2)
A_5 = dual_face(L_1, K_1, P_1)
B_5 = dual_face(M_1, L_1, E_1)
C_5 = dual_face(P_1, M_1, N_1)
D_5 = dual_face(N_1, O_1, Q_1)
E_5 = dual_face(Q_1, Q_2, L)
F_5 = dual_face(L, K, J)
G_5 = dual_face(K, T_2, Q_3)
H_5 = dual_face(T_2, S_2, P_3)
I_5 = dual_face(S_2, R_2, K_3)
J_5 = dual_face(R_2, P_2, O_2)
K_5 = dual_face(P_1, P_2, O_2)
L_5 = dual_face(D_1, F_1, E_1)
M_5 = dual_face(F_1, O_1, Q_1)
N_5 = dual_face(R_1, U_2, V_2)
O_5 = dual_face(U_2, I, J)
P_5 = dual_face(S_3, V_4, S_4)
Q_5 = dual_face(V_4, Q_3, P_3)
R_5 = dual_face(O_3, L_3, M_3)
S_5 = dual_face(L_3, K_3, O_2)
T_5 = dual_face(K_1, L_1, E_1)
U_5 = dual_face(C_1, D_1, A)
V_5 = dual_face(T_1, S_1, V_2)
W_5 = dual_face(S_4, T_4, U_4)
Z_5 = dual_face(U_4, Z_4, W_4)
A_6 = dual_face(Z_3, W_3, V)
B_6 = dual_face(V, U, B_3)
C_6 = dual_face(V_3, W_3, Z_3)
D_6 = dual_face(R_3, B_3, Z_2)
E_6 = dual_face(V_1, A_2, T_1)
F_6 = dual_face(T_1, S_1, R_1)
G_6 = dual_face(A_2, Z_2, B_3)
H_6 = dual_face(Z, U, V)
I_6 = dual_face(W, Z, C_3)
J_6 = dual_face(C_3, D_3, E_3)
K_6 = dual_face(A_3, B_2, C_2)
L_6 = dual_face(Z_1, W_1, A_3)
M_6 = dual_face(W_1, Z_1, C)
N_6 = dual_face(C, D, A)
O_6 = dual_face(C, Z_1, B_2)
P_6 = dual_face(D_2, C_2, K_2)
Q_6 = dual_face(K_2, E_3, F_3)
R_6 = dual_face(B_4, A_4, F_4)
S_6 = dual_face(W_4, F, G)
T_6 = dual_face(G, H, E)
U_6 = dual_face(J_4, Q_4, R_4)
V_6 = dual_face(F_4, I_4, J_4)
W_6 = dual_face(D_4, G_4, H_4)
Z_6 = dual_face(H_4, K_4, L_4)
A_7 = dual_face(G_3, K_4, L_4)
B_7 = dual_face(K_4, H_4, E_4)
C_7 = dual_face(P, O, N)
D_7 = dual_face(L_4, M_4, N_4)
E_7 = dual_face(M_4, P_4, O_4)
F_7 = dual_face(P_4, H, E)
G_7 = dual_face(Q, R, S)
H_7 = dual_face(S, N_2, M_2)
I_7 = dual_face(N_2, J_3, I_3)
J_7 = dual_face(H_3, I_3, M_2)
K_7 = dual_face(L_2, H_2, I_1)
L_7 = dual_face(H_2, G_2, F_2)
M_7 = dual_face(G_2, I_2, E_2)
N_7 = dual_face(M, P, J_2)
O_7 = dual_face(H_1, G_1, B_1)
t1, i_{18}, j_{18}, k_{18} = Polygon(G_6, M_6, E_6)
t2, l_{18}, m_{18}, n_{18} = Polygon(G_6, E_6, V_5)
t3, p_{18}, q_{18}, r_{18} = Polygon(G_6, V_5, D_6)
t4, s_{18}, t_{18}, a_{18} = Polygon(G_6, D_6, B_6)
t5, b_{18}, c_{18}, d_{18} = Polygon(G_6, B_6, H_6)
t6, e_{18}, f_{19}, g_{19} = Polygon(G_6, H_6, I_6)
t7, h_{19}, i_{19}, j_{19} = Polygon(G_6, I_6, J_6)
t8, k_{19}, l_{19}, m_{19} = Polygon(G_6, J_6, K_6)
t9, n_{19}, p_{19}, q_{19} = Polygon(G_6, K_6, L_6)
t10, r_{19}, s_{19}, t_{19} = Polygon(G_6, L_6, M_6)
t11, a_{19}, b_{19}, c_{19} = Polygon(A_6, H_6, B_6)
t12, d_{19}, e_{19}, f_{20} = Polygon(A_6, B_6, C_6)
t13, g_{20}, h_{20}, i_{20} = Polygon(A_6, C_6, W_5)
t14, z_5, j_{20}, k_{20} = Polygon(A_6, W_5, Z_5)
t15, l_{20}, m_{20}, n_{20} = Polygon(A_6, Z_5, S_6)
t16, u_6, p_{20}, q_{20} = Polygon(A_6, S_6, U_6)
t17, v_6, r_{20}, s_{20} = Polygon(A_6, U_6, V_6)
t18, t_{20}, a_{20}, b_{20} = Polygon(A_6, V_6, R_6)
t19, c_{20}, d_{20}, e_{20} = Polygon(A_6, R_6, I_6)
t20, f_{21}, g_{21}, h_{21} = Polygon(A_6, I_6, H_6)
t21, i_{21}, j_{21}, k_{21} = Polygon(O_5, W_5, C_6)
t22, l_{21}, m_{21}, n_{21} = Polygon(O_5, C_6, B_6)
t23, p_{21}, q_{21}, r_{21} = Polygon(O_5, B_6, D_6)
t24, s_{21}, t_{21}, a_{21} = Polygon(O_5, D_6, V_5)
t25, b_{21}, c_{21}, d_{21} = Polygon(O_5, V_5, N_5)
t26, e_{21}, f_{22}, g_{22} = Polygon(O_5, N_5, E_5)
t27, h_{22}, i_{22}, j_{22} = Polygon(O_5, E_5, F_5)
t28, k_{22}, l_{22}, m_{22} = Polygon(O_5, F_5, G_5)
t29, n_{22}, p_{22}, q_{22} = Polygon(O_5, G_5, P_5)
t30, r_{22}, s_{22}, t_{22} = Polygon(O_5, P_5, W_5)
t31, a_{22}, b_{22}, c_{22} = Polygon(Q_5, T_6, S_6)
t32, d_{22}, e_{22}, f_{23} = Polygon(Q_5, S_6, Z_5)
t33, g_{23}, h_{23}, i_{23} = Polygon(Q_5, Z_5, W_5)
t34, j_{23}, k_{23}, l_{23} = Polygon(Q_5, W_5, P_5)
t35, m_{23}, n_{23}, p_{23} = Polygon(Q_5, P_5, G_5)
t36, q_{23}, r_{23}, s_{23} = Polygon(Q_5, G_5, H_5)
t37, t_{23}, a_{23}, b_{23} = Polygon(Q_5, H_5, I_5)
t38, c_{23}, d_{23}, e_{23} = Polygon(Q_5, I_5, R_5)
t39, f_{24}, g_{24}, h_{24} = Polygon(Q_5, R_5, F_7)
t40, i_{24}, j_{24}, k_{24} = Polygon(Q_5, F_7, T_6)
t41, l_{24}, m_{24}, n_{24} = Polygon(H_5, C_5, G_5)
t42, p_{24}, q_{24}, r_{24} = Polygon(C_5, G_5, F_5)
t43, s_{24}, t_{24}, a_{24} = Polygon(C_5, F_5, E_5)
t44, b_{24}, c_{24}, d_{24} = Polygon(C_5, E_5, D_5)
t45, e_{24}, f_{25}, g_{25} = Polygon(C_5, D_5, B_5)
t46, h_{25}, i_{25}, j_{25} = Polygon(C_5, B_5, A_5)
t47, k_{25}, l_{25}, m_{25} = Polygon(C_5, A_5, K_5)
t48, n_{25}, p_{25}, q_{25} = Polygon(C_5, K_5, J_5)
t49, r_{25}, s_{25}, t_{25} = Polygon(C_5, J_5, I_5)
t50, a_{25}, b_{25}, c_{25} = Polygon(C_5, I_5, H_5)
t51, d_{25}, e_{25}, f_{26} = Polygon(S_5, F_7, R_5)
t52, g_{26}, h_{26}, i_{26} = Polygon(S_5, R_5, I_5)
t53, j_{26}, k_{26}, l_{26} = Polygon(S_5, I_5, J_5)
t54, m_{26}, n_{26}, p_{26} = Polygon(S_5, J_5, K_5)
t55, q_{26}, r_{26}, s_{26} = Polygon(S_5, K_5, G_7)
t56, t_{26}, a_{26}, b_{26} = Polygon(S_5, G_7, H_7)
t57, c_{26}, d_{26}, e_{26} = Polygon(S_5, H_7, I_7)
t58, f_{27}, g_{27}, h_{27} = Polygon(S_5, I_7, D_7)
t59, i_{27}, j_{27}, k_{27} = Polygon(S_5, D_7, E_7)
t60, l_{27}, m_{27}, n_{27} = Polygon(S_5, E_7, F_7)
t61, p_{27}, z_6, q_{27} = Polygon(Z_6, T_6, F_7)
t62, r_{27}, s_{27}, t_{27} = Polygon(Z_6, F_7, E_7)
t63, a_{27}, b_{27}, c_{27} = Polygon(Z_6, E_7, D_7)
t64, d_{27}, e_{27}, f_{28} = Polygon(Z_6, D_7, A_7)
t65, g_{28}, h_{28}, i_{28} = Polygon(Z_6, A_7, B_7)
t66, w_6, j_{28}, k_{28} = Polygon(Z_6, B_7, W_6)
t67, l_{28}, m_{28}, n_{28} = Polygon(Z_6, W_6, V_6)
t68, p_{28}, q_{28}, r_{28} = Polygon(Z_6, V_6, U_6)
t69, s_{28}, t_{28}, a_{28} = Polygon(Z_6, U_6, S_6)
t70, b_{28}, c_{28}, d_{28} = Polygon(Z_6, S_6, T_6)
t71, e_{28}, f_{29}, g_{29} = Polygon(P_6, Q_6, N_7)
t72, h_{29}, i_{29}, j_{29} = Polygon(P_6, K_6, Q_6)
t73, k_{29}, l_{29}, m_{29} = Polygon(Q_6, K_6, J_6)
t74, n_{29}, p_{29}, q_{29} = Polygon(Q_6, J_6, I_6)
t75, r_{29}, s_{29}, t_{29} = Polygon(Q_6, I_6, R_6)
t76, a_{29}, b_{29}, c_{29} = Polygon(Q_6, R_6, V_6)
t77, d_{29}, e_{29}, f_{30} = Polygon(Q_6, V_6, W_6)
t78, g_{30}, h_{30}, i_{30} = Polygon(Q_6, W_6, B_7)
t79, j_{30}, k_{30}, l_{30} = Polygon(Q_6, B_7, C_7)
t80, m_{30}, n_{30}, p_{30} = Polygon(Q_6, C_7, N_7)
t81, q_{30}, r_{30}, s_{30} = Polygon(J_7, A_7, D_7)
t82, t_{30}, a_{30}, b_{30} = Polygon(J_7, D_7, I_7)
t83, c_{30}, d_{30}, e_{30} = Polygon(J_7, I_7, H_7)
t84, f_{31}, g_{31}, h_{31} = Polygon(J_7, H_7, K_7)
t85, i_{31}, j_{31}, k_{31} = Polygon(J_7, K_7, L_7)
t86, l_{31}, m_{31}, n_{31} = Polygon(J_7, L_7, M_7)
t87, p_{31}, q_{31}, r_{31} = Polygon(J_7, M_7, N_7)
t88, s_{31}, t_{31}, a_{31} = Polygon(J_7, C_7, N_7)
t89, b_{31}, c_{31}, d_{31} = Polygon(J_7, C_7, B_7)
t90, e_{31}, f_{32}, g_{32} = Polygon(J_7, B_7, A_7)
t91, h_{32}, i_{32}, o_6 = Polygon(N_6, O_6, M_6)
t92, j_{32}, k_{32}, l_{32} = Polygon(O_6, M_6, L_6)
t93, m_{32}, n_{32}, p_{32} = Polygon(O_6, L_6, K_6)
t94, q_{32}, r_{32}, s_{32} = Polygon(O_6, K_6, P_6)
t95, t_{32}, a_{32}, b_{32} = Polygon(O_6, P_6, N_7)
t96, c_{32}, d_{32}, e_{32} = Polygon(O_6, N_7, M_7)
t97, f_{33}, g_{33}, h_{33} = Polygon(O_6, M_7, L_7)
t98, o_7, i_{33}, j_{33} = Polygon(O_6, L_7, O_7)
t99, u_5, k_{33}, l_{33} = Polygon(O_6, O_7, U_5)
t100, m_{33}, n_{33}, p_{33} = Polygon(O_6, U_5, N_6)
t101, q_{33}, r_{33}, s_{33} = Polygon(T_5, G_7, K_5)
t102, t_{33}, a_{33}, b_{33} = Polygon(T_5, K_5, A_5)
t103, c_{33}, d_{33}, e_{33} = Polygon(T_5, A_5, B_5)
t104, f_{34}, g_{34}, h_{34} = Polygon(T_5, B_5, L_5)
t105, i_{34}, j_{34}, k_{34} = Polygon(T_5, L_5, U_5)
t106, l_{34}, m_{34}, n_{34} = Polygon(T_5, U_5, O_7)
t107, p_{34}, q_{34}, r_{34} = Polygon(T_5, O_7, L_7)
t108, s_{34}, t_{34}, a_{34} = Polygon(T_5, L_7, K_7)
t109, b_{34}, c_{34}, d_{34} = Polygon(T_5, K_7, H_7)
t110, e_{34}, f_{35}, g_{35} = Polygon(T_5, H_7, G_7)
t111, h_{35}, i_{35}, j_{35} = Polygon(F_6, E_5, N_5)
t112, k_{35}, l_{35}, m_{35} = Polygon(F_6, N_5, V_5)
t113, n_{35}, p_{35}, q_{35} = Polygon(F_6, V_5, E_6)
t114, r_{35}, s_{35}, t_{35} = Polygon(F_6, E_6, M_6)
t115, a_{35}, b_{35}, c_{35} = Polygon(F_6, M_6, N_6)
t116, d_{35}, e_{35}, f_{36} = Polygon(F_6, N_6, U_5)
t117, g_{36}, h_{36}, i_{36} = Polygon(F_6, U_5, L_5)
t118, j_{36}, k_{36}, l_{36} = Polygon(F_6, L_5, B_5)
t119, m_{36}, n_{36}, p_{36} = Polygon(F_6, B_5, D_5)
t120, q_{36}, r_{36}, s_{36} = Polygon(F_6, D_5, E_5)

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})