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

valider

valider

valider

S =

F =

A =

a: 0.8
sommets: 62
faces: 60
aretes: 120
rep1: 0
rep2: 0
rep3: 0
ChampTexte1 = Textfield(rep1)
ChampTexte2 = Textfield(rep2)
ChampTexte3 = Textfield(rep3)
p: (1 + sqrt(5)) / 2
b: (a * p^(2))
c: (a * p^(3))
d: ((a * 2) * p)
e: (a * (p + 2))
f: (a * p)
l1 = Sequence(Sequence[Sequence[((a * (-1)^(i)), (a * (-1)^(j)), (c * (-1)^(k))), k, 1, 2], j, 1, 2], i, 1, 2)
l4 = Sequence(Sequence[Sequence[((b * (-1)^(i)), (f * (-1)^(j)), (d * (-1)^(k))), k, 1, 2], j, 1, 2], i, 1, 2)
l5 = Sequence(Sequence[Sequence[((d * (-1)^(k)), (b * (-1)^(i)), (f * (-1)^(j))), k, 1, 2], j, 1, 2], i, 1, 2)
l6 = Sequence(Sequence[Sequence[((f * (-1)^(j)), (d * (-1)^(k)), (b * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l2 = Sequence(Sequence[Sequence[((c * (-1)^(k)), (a * (-1)^(j)), (a * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l3 = Sequence(Sequence[Sequence[((a * (-1)^(j)), (c * (-1)^(k)), (a * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l7 = Sequence(Sequence[Sequence[((e * (-1)^(i)), 0^(j), (b * (-1)^(k))), k, 1, 2], j, 1, 2], i, 1, 2)
l8 = Sequence(Sequence[Sequence[((b * (-1)^(k)), (e * (-1)^(i)), 0^(j)), k, 1, 2], j, 1, 2], i, 1, 2)
l9 = Sequence(Sequence[Sequence[(0^(j), (b * (-1)^(k)), (e * (-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(l9)
F = Point(l4)
G = Point(l7)
H = Point(l4)
I = Point(l6)
J = Point(l9)
K = Point(l6)
L = Point(l6)
M = Point(l4)
N = Point(l7)
O = Point(l4)
P = Point(l6)
Q = Point(l3)
R = Point(l3)
S = Point(l3)
T = Point(l3)
U = Point(l5)
V = Point(l8)
W = Point(l2)
Z = Point(l5)
A_1 = Point(l2)
B_1 = Point(l2)
C_1 = Point(l5)
D_1 = Point(l8)
E_1 = Point(l2)
F_1 = Point(l5)
G_1 = Point(l5)
H_1 = Point(l8)
I_1 = Point(l2)
J_1 = Point(l5)
K_1 = Point(l2)
L_1 = Point(l2)
M_1 = Point(l5)
N_1 = Point(l8)
O_1 = Point(l2)
P_1 = Point(l5)
Q_1 = Point(l3)
R_1 = Point(l6)
S_1 = Point(l3)
T_1 = Point(l9)
U_1 = Point(l6)
V_1 = Point(l4)
W_1 = Point(l7)
Z_1 = Point(l4)
A_2 = Point(l3)
B_2 = Point(l6)
C_2 = Point(l3)
D_2 = Point(l6)
E_2 = Point(l9)
F_2 = Point(l1)
G_2 = Point(l4)
H_2 = Point(l7)
I_2 = Point(l4)
J_2 = Point(l1)
K_2 = Point(l1)
L_2 = Point(l1)
Z2: (0, 0, 0)
M_2 = dual_face(M, L, U)
N_2 = dual_face(L, T, V)
O_2 = dual_face(U, V, Z)
P_2 = dual_face(M, U, W)
Q_2 = dual_face(W, A_1, E_1)
R_2 = dual_face(B_1, W, N)
S_2 = dual_face(N, M, D)
T_2 = dual_face(D, J, L)
U_2 = dual_face(L, T, S)
V_2 = dual_face(K, J, C)
W_2 = dual_face(B, C, H)
Z_2 = dual_face(D, C, J)
A_3 = dual_face(A, B, C)
B_3 = dual_face(A, B, E)
C_3 = dual_face(E, I, F)
D_3 = dual_face(F, G, I_1)
E_3 = dual_face(I_1, L_1, G)
F_3 = dual_face(G, H, M_1)
G_3 = dual_face(M_1, K, H)
H_3 = dual_face(S, N_1, M_1)
I_3 = dual_face(S, Q_1, N_1)
J_3 = dual_face(Q_1, R_1, P_1)
K_3 = dual_face(I_2, R_1, P_1)
L_3 = dual_face(P_1, O_1, H_2)
M_3 = dual_face(K_1, H_2, O_1)
N_3 = dual_face(O_1, L_1, I_1)
O_3 = dual_face(L_1, M_1, N_1)
P_3 = dual_face(G_1, F, I)
Q_3 = dual_face(I, R, H_1)
R_3 = dual_face(H_1, J_1, K_1)
S_3 = dual_face(H_1, C_2, D_2)
T_3 = dual_face(I, R, Q)
U_3 = dual_face(Q, R, C_2)
V_3 = dual_face(C_2, D_2, E_2)
W_3 = dual_face(J_1, G_2, D_2)
Z_3 = dual_face(G_2, K_2, E_2)
A_4 = dual_face(E_2, F_2, K_2)
B_4 = dual_face(B_2, E_2, F_2)
C_4 = dual_face(B_2, Z_1, F_1)
D_4 = dual_face(D_1, A_2, B_2)
E_4 = dual_face(H_2, G_2, J_1)
F_4 = dual_face(G_2, K_2, J_2)
G_4 = dual_face(J_2, T_1, L_2)
H_4 = dual_face(L_2, J_2, K_2)
I_4 = dual_face(I_2, J_2, T_1)
J_4 = dual_face(L_2, F_2, Z_1)
K_4 = dual_face(Z_1, W_1, E_1)
L_4 = dual_face(E_1, A_1, W_1)
M_4 = dual_face(W_1, V_1, Z)
N_4 = dual_face(Z, U_1, V_1)
O_4 = dual_face(V_1, L_2, T_1)
P_4 = dual_face(E_1, F_1, D_1)
Q_4 = dual_face(C_1, B_1, N)
R_4 = dual_face(O, C_1, P)
S_4 = dual_face(A, O, P)
T_4 = dual_face(Q, D_1, C_1)
U_4 = dual_face(A_2, D_1, Q)
V_4 = dual_face(S_1, U_1, T_1)
W_4 = dual_face(Z2, Q_1, S)
Z_4 = dual_face(S_1, Q_1, S)
A_5 = dual_face(T, S_1, V)
B_5 = dual_face(V, Z, U_1)
C_5 = dual_face(A, A_1, B)
D_5 = dual_face(B_1, B, A_2)
q31, e_{11}, f_{12}, g_{12}, h_{12} = Polygon(A_3, Z_2, V_2, W_2)
q32, i_{12}, j_{12}, k_{12}, l_{12} = Polygon(W_2, V_2, G_3, F_3)
q33, m_{12}, n_{12}, p_{12}, q_{12} = Polygon(W_2, F_3, E_3, D_3)
q34, r_{12}, s_{12}, t_{12}, a_{12} = Polygon(W_2, D_3, P_3, C_3)
q35, b_{12}, c_{12}, d_{12}, e_{12} = Polygon(W_2, C_3, B_3, A_3)
q36, f_{13}, g_{13}, h_{13}, i_{13} = Polygon(R_3, D_3, P_3, Q_3)
E_5 = dual_face(H_1, C_2, R)
q37, j_{13}, k_{13}, l_{13}, m_{13} = Polygon(R_3, D_3, E_3, N_3)
q38, n_{13}, p_{13}, q_{13}, r_{13} = Polygon(R_3, N_3, M_3, E_4)
q39, s_{13}, t_{13}, a_{13}, b_{13} = Polygon(R_3, E_4, W_3, S_3)
q40, c_{13}, d_{13}, e_{13}, f_{14} = Polygon(R_3, S_3, E_5, Q_3)
q41, g_{14}, h_{14}, i_{14}, j_{14} = Polygon(F_4, E_4, M_3, L_3)
q42, k_{14}, l_{14}, m_{14}, n_{14} = Polygon(F_4, L_3, K_3, I_4)
q43, p_{14}, q_{14}, r_{14}, s_{14} = Polygon(F_4, I_4, G_4, H_4)
q44, t_{14}, a_{14}, b_{14}, c_{14} = Polygon(F_4, H_4, A_4, Z_3)
q45, d_{14}, e_{14}, f_{15}, g_{15} = Polygon(F_4, Z_3, W_3, E_4)
q46, h_{15}, i_{15}, j_{15}, k_{15} = Polygon(U_3, E_5, S_3, V_3)
q47, l_{15}, u_4, m_{15}, n_{15} = Polygon(U_3, U_4, D_4, V_3)
q48, p_{15}, q_{15}, r_{15}, s_{15} = Polygon(V_3, D_4, C_4, B_4)
q49, t_{15}, a_{15}, b_{15}, c_{15} = Polygon(V_3, B_4, A_4, Z_3)
q50, d_{15}, e_{15}, f_{16}, g_{16} = Polygon(V_3, Z_3, W_3, S_3)
q51, h_{16}, i_{16}, j_{16}, k_{16} = Polygon(T_3, U_3, E_5, Q_3)
q52, l_{16}, m_{16}, n_{16}, p_{16} = Polygon(T_3, Q_3, P_3, C_3)
q53, q_{16}, r_{16}, s_{16}, t_{16} = Polygon(T_3, C_3, B_3, S_4)
q54, a_{16}, b_{16}, c_{16}, d_{16} = Polygon(T_3, S_4, R_4, T_4)
q55, e_{16}, f_{17}, g_{17}, h_{17} = Polygon(T_3, T_4, U_4, U_3)
q56, i_{17}, j_{17}, k_{17}, l_{17} = Polygon(P_4, D_4, U_4, T_4)
q57, m_{17}, n_{17}, p_{17}, q_{17} = Polygon(P_4, T_4, R_4, Q_4)
q58, r_{17}, s_{17}, t_{17}, a_{17} = Polygon(P_4, Q_4, R_2, Q_2)
q59, b_{17}, c_{17}, d_{17}, e_{17} = Polygon(P_4, Q_2, L_4, K_4)
q60, f_{18}, g_{18}, h_{18}, i_{18} = Polygon(P_4, K_4, C_4, D_4)
q61, j_{18}, k_{18}, l_{18}, m_{18} = Polygon(A_3, S_2, S_4, B_3)
q62, n_{18}, p_{18}, q_{18}, r_{18} = Polygon(S_2, S_4, R_4, Q_4)
q63, s_{18}, t_{18}, a_{18}, b_{18} = Polygon(S_2, Q_4, R_2, P_2)
q64, c_{18}, d_{18}, e_{18}, f_{19} = Polygon(S_2, P_2, M_2, T_2)
q65, g_{19}, h_{19}, i_{19}, j_{19} = Polygon(S_2, T_2, Z_2, A_3)
q66, k_{19}, l_{19}, m_{19}, n_{19} = Polygon(O_2, P_2, R_2, Q_2)
q67, p_{19}, q_{19}, r_{19}, s_{19} = Polygon(O_2, Q_2, L_4, M_4)
q68, t_{19}, a_{19}, b_{19}, c_{19} = Polygon(O_2, M_4, N_4, B_5)
q69, d_{19}, e_{19}, f_{20}, g_{20} = Polygon(O_2, B_5, A_5, N_2)
q70, h_{20}, i_{20}, j_{20}, k_{20} = Polygon(O_2, P_2, M_2, N_2)
q71, l_{20}, m_{20}, n_{20}, p_{20} = Polygon(U_2, N_2, M_2, T_2)
q72, q_{20}, r_{20}, s_{20}, t_{20} = Polygon(U_2, T_2, Z_2, V_2)
q73, a_{20}, b_{20}, c_{20}, d_{20} = Polygon(U_2, V_2, G_3, H_3)
q74, e_{20}, f_{21}, g_{21}, h_{21} = Polygon(U_2, H_3, I_3, Z_4)
q75, i_{21}, j_{21}, k_{21}, l_{21} = Polygon(U_2, Z_4, A_5, N_2)
q76, m_{21}, n_{21}, p_{21}, q_{21} = Polygon(O_3, H_3, G_3, F_3)
q77, r_{21}, s_{21}, t_{21}, a_{21} = Polygon(O_3, J_3, I_3, H_3)
q78, b_{21}, c_{21}, d_{21}, e_{21} = Polygon(O_3, F_3, E_3, N_3)
q79, f_{22}, g_{22}, h_{22}, i_{22} = Polygon(O_3, N_3, M_3, L_3)
q80, j_{22}, k_{22}, l_{22}, m_{22} = Polygon(O_3, L_3, K_3, J_3)
q81, v_4, n_{22}, p_{22}, q_{22} = Polygon(V_4, J_3, I_3, Z_4)
q82, r_{22}, s_{22}, t_{22}, a_{22} = Polygon(V_4, Z_4, A_5, B_5)
q83, b_{22}, c_{22}, d_{22}, o_4 = Polygon(V_4, B_5, N_4, O_4)
q84, e_{22}, f_{23}, g_{23}, h_{23} = Polygon(V_4, O_4, G_4, I_4)
q85, i_{23}, j_{23}, k_{23}, l_{23} = Polygon(V_4, I_4, K_3, J_3)
q86, m_{23}, n_{23}, p_{23}, q_{23} = Polygon(J_4, M_4, L_4, K_4)
q87, r_{23}, s_{23}, t_{23}, a_{23} = Polygon(J_4, K_4, C_4, B_4)
q88, b_{23}, c_{23}, d_{23}, e_{23} = Polygon(J_4, B_4, A_4, H_4)
q89, f_{24}, g_{24}, h_{24}, i_{24} = Polygon(J_4, H_4, G_4, O_4)
q90, j_{24}, k_{24}, l_{24}, m_{24} = Polygon(J_4, O_4, N_4, M_4)

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)

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})