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

valider

valider

valider

S =

F =

A =

r: 0.7
sommets: 92
faces: 60
aretes: 150
rep1: 0
rep2: 0
rep3: 0
ChampTexte1 = Textfield(rep1)
ChampTexte2 = Textfield(rep2)
ChampTexte3 = Textfield(rep3)
p: (1 + sqrt(5)) / 2
q: 1.7155615
s: q - 1 / q
t: (q * p) + (p * p) + p / q
a: (r * s)
b: (r * t)
c: (r * (s + t / p + p))
d: (r * ((-((s * p))) + t + 1 / p))
e: (r * (s / p + (t * p) - 1))
l4 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((c * (-1)^(i)), (d * (-1)^(j)), (e * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l6 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((d * (-1)^(i)), (e * (-1)^(j)), (c * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
f: (r * (((-s)) / p + (t * p) + 1))
g: (r * ((-s) + t / p - p))
h: (r * ((s * p) + t - 1 / p))
l7 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((f * (-1)^(i)), (g * (-1)^(j)), (h * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l8 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((h * (-1)^(i)), (f * (-1)^(j)), (g * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l: (r * (((-s)) / p + (t * p) - 1))
m: (r * (s - t / p - p))
n: (r * ((s * p) + t + 1 / p))
l10 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((l * (-1)^(i)), (m * (-1)^(j)), (n * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l11 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((n * (-1)^(i)), (l * (-1)^(j)), (m * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l12 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((m * (-1)^(i)), (n * (-1)^(j)), (l * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
u: (r * (s + t / p - p))
v: (r * ((s * p) - t + 1 / p))
w: (r * (s / p + (t * p) + 1))
l13 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((u * (-1)^(i)), (v * (-1)^(j)), (w * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l14 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((w * (-1)^(i)), (u * (-1)^(j)), (v * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l15 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((v * (-1)^(i)), (w * (-1)^(j)), (u * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l1 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, (((2 * a) * (-1)^(i)), (2 * (r * (-1)^(j))), ((2 * b) * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l2 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, (((2 * b) * (-1)^(i)), ((2 * a) * (-1)^(j)), (2 * (r * (-1)^(k))))], k, 1, 2], j, 1, 2], i, 1, 2)
l3 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((2 * (r * (-1)^(i))), ((2 * b) * (-1)^(j)), ((2 * a) * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l9 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((g * (-1)^(i)), (h * (-1)^(j)), (f * (-1)^(k)))], k, 1, 2], j, 1, 2], i, 1, 2)
l5 = Sequence(Sequence[Sequence[If[(-1)^(i + j + k) < 0, ((e * (-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(l13)
D = Point(l9)
E = Point(l4)
F = Point(l7)
G = Point(l10)
H = Point(l13)
I = Point(l9)
J = Point(l12)
K = Point(l11)
L = Point(l14)
M = Point(l2)
N = Point(l5)
O = Point(l6)
P = Point(l12)
Q = Point(l15)
R = Point(l3)
S = Point(l8)
T = Point(l15)
U = Point(l3)
V = Point(l8)
W = Point(l11)
Z = Point(l10)
A_1 = Point(l7)
B_1 = Point(l4)
C_1 = Point(l6)
D_1 = Point(l15)
E_1 = Point(l3)
F_1 = Point(l5)
G_1 = Point(l8)
H_1 = Point(l15)
I_1 = Point(l3)
J_1 = Point(l8)
K_1 = Point(l5)
L_1 = Point(l2)
M_1 = Point(l6)
N_1 = Point(l9)
O_1 = Point(l12)
P_1 = Point(l11)
Q_1 = Point(l2)
R_1 = Point(l14)
S_1 = Point(l14)
T_1 = Point(l2)
U_1 = Point(l5)
V_1 = Point(l7)
W_1 = Point(l10)
Z_1 = Point(l6)
A_2 = Point(l9)
B_2 = Point(l12)
C_2 = Point(l11)
D_2 = Point(l14)
E_2 = Point(l7)
F_2 = Point(l10)
G_2 = Point(l13)
H_2 = Point(l1)
I_2 = Point(l4)
J_2 = Point(l13)
K_2 = Point(l4)
L_2 = Point(l1)
M_2 = dual_face(B_1, F_1, A_1)
N_2 = dual_face(F_1, G_1, P_1)
O_2 = dual_face(F_1, Q_1, A_1)
P_2 = dual_face(Q_1, S_1, A_1)
Q_2 = dual_face(Q_1, T_1, S_1)
R_2 = dual_face(Q_1, R_1, T_1)
S_2 = dual_face(R_1, V_1, T_1)
T_2 = dual_face(R_1, W_1, V_1)
U_2 = dual_face(P_1, W_1, R_1)
V_2 = dual_face(P_1, O_1, W_1)
W_2 = dual_face(H_1, O_1, P_1)
Z_2 = dual_face(G_1, H_1, P_1)
A_3 = dual_face(C_1, G_1, F_1)
B_3 = dual_face(C_1, F_1, B_1)
C_3 = dual_face(A_1, S_1, Z)
D_3 = dual_face(S_1, W, Z)
E_3 = dual_face(S_1, T_1, U_1)
F_3 = dual_face(U_1, V_1, T_1)
G_3 = dual_face(K_2, U_1, V_1)
H_3 = dual_face(V_1, W_1, J_2)
I_3 = dual_face(J_2, W_1, O_1)
J_3 = dual_face(H_1, E_1, G_1)
K_3 = dual_face(I_1, H_1, E_1)
L_3 = dual_face(C_1, I, J)
M_3 = dual_face(I, B_1, B)
N_3 = dual_face(B, H, I)
O_3 = dual_face(A, B, H)
P_3 = dual_face(B, C, A)
Q_3 = dual_face(C, D, A)
R_3 = dual_face(C, Z, P)
S_3 = dual_face(Z, W, P)
T_3 = dual_face(W, V, Q)
U_3 = dual_face(Z, A_1, B_1)
V_3 = dual_face(V, Z_1, U_1)
W_3 = dual_face(U_1, K_2, V_3)
Z_3 = dual_face(Z_1, K_2, U_1)
A_4 = dual_face(Z_1, K_2, A_2)
B_4 = dual_face(A_2, L_2, K_2)
C_4 = dual_face(Z_1, U, V)
D_4 = dual_face(V, Q, U)
E_4 = dual_face(U, R, Q)
F_4 = dual_face(U, T, R)
G_4 = dual_face(T, S, R)
H_4 = dual_face(T, C_2, S)
I_4 = dual_face(B_2, C_2, T)
J_4 = dual_face(B_2, F_2, C_2)
K_4 = dual_face(B_2, G_2, F_2)
L_4 = dual_face(A_2, G_2, B_2)
M_4 = dual_face(L_2, H_2, G_2)
N_4 = dual_face(L_2, J_2, H_2)
O_4 = dual_face(A_2, B_2, T)
P_4 = dual_face(G_2, H_2, I_2)
Q_4 = dual_face(F_2, D_2, C_2)
R_4 = dual_face(D_2, F_2, E_2)
S_4 = dual_face(N, S, C_2)
T_4 = dual_face(O, S, N)
U_4 = dual_face(O, R, Q)
V_4 = dual_face(Q, P, W)
W_4 = dual_face(D, P, C)
Z_4 = dual_face(H, A, E)
A_5 = dual_face(A, D, E)
B_5 = dual_face(D, O, E)
C_5 = dual_face(E, O, N)
D_5 = dual_face(D_2, E_2, L_1)
E_5 = dual_face(L_1, M, D_2)
F_5 = dual_face(M, L_1, L)
G_5 = dual_face(L, M, F)
H_5 = dual_face(F, N, M)
I_5 = dual_face(E, N, F)
J_5 = dual_face(F, G, L)
K_5 = dual_face(L, K, G)
L_5 = dual_face(L, L_1, K_1)
M_5 = dual_face(L_1, E_2, K_1)
N_5 = dual_face(E_2, I_2, K_1)
O_5 = dual_face(K_1, M_1, I_2)
P_5 = dual_face(I_2, H_2, N_1)
Q_5 = dual_face(M_1, I_2, N_1)
R_5 = dual_face(N_1, J_2, H_2)
S_5 = dual_face(M_1, N_1, O_1)
T_5 = dual_face(I_1, M_1, J_1)
U_5 = dual_face(J_1, D_1, I_1)
V_5 = dual_face(G, J, H)
W_5 = dual_face(H, J, I)
Z_5 = dual_face(I, B_1, C_1)
A_6 = dual_face(D_1, J, K)
B_6 = dual_face(K, J_1, D_1)
C_6 = dual_face(E_1, G_1, C_1)
poly13, l_{15}, m_{15}, n_{15}, p_{15}, q_{15} = Polygon(S_4, H_5, I_5, C_5, T_4)
poly14, r_{15}, s_{15}, t_{15}, a_{15}, b_{15} = Polygon(S_4, H_5, G_5, F_5, E_5)
poly15, c_{15}, d_{15}, e_{15}, f_{16}, g_{16} = Polygon(S_4, E_5, D_5, R_4, Q_4)
poly16, h_{16}, i_{16}, j_{16}, k_{16}, l_{16} = Polygon(S_4, Q_4, J_4, I_4, H_4)
D_6 = dual_face(S, O, R)
poly17, m_{16}, n_{16}, p_{16}, q_{16}, r_{16} = Polygon(S_4, H_4, G_4, D_6, T_4)
poly18, s_{16}, t_{16}, a_{16}, b_{16}, c_{16} = Polygon(O_4, I_4, H_4, G_4, F_4)
poly19, d_{16}, e_{16}, f_{17}, g_{17}, h_{17} = Polygon(O_4, I_4, J_4, K_4, L_4)
E_6 = dual_face(G_2, A_2, L_2)
poly20, i_{17}, j_{17}, k_{17}, l_{17}, m_{17} = Polygon(O_4, L_4, E_6, B_4, A_4)
poly21, n_{17}, p_{17}, q_{17}, r_{17}, s_{17} = Polygon(O_4, A_4, Z_3, V_3, C_4)
poly22, t_{17}, a_{17}, b_{17}, c_{17}, d_{17} = Polygon(O_4, C_4, D_4, E_4, F_4)
poly23, e_{17}, f_{18}, g_{18}, h_{18}, i_{18} = Polygon(E_3, V_3, C_4, D_4, T_3)
poly24, j_{18}, k_{18}, l_{18}, m_{18}, n_{18} = Polygon(E_3, T_3, V_4, S_3, D_3)
poly25, p_{18}, q_{18}, r_{18}, s_{18}, t_{18} = Polygon(E_3, D_3, C_3, P_2, Q_2)
poly26, a_{18}, b_{18}, c_{18}, d_{18}, e_{18} = Polygon(E_3, Q_2, R_2, S_2, F_3)
poly27, f_{19}, g_{19}, h_{19}, i_{19}, j_{19} = Polygon(E_3, F_3, G_3, Z_3, V_3)
poly28, k_{19}, l_{19}, m_{19}, n_{19}, p_{19} = Polygon(H_3, N_4, M_4, E_6, B_4)
poly29, q_{19}, r_{19}, s_{19}, t_{19}, a_{19} = Polygon(H_3, B_4, A_4, Z_3, G_3)
poly30, b_{19}, c_{19}, d_{19}, e_{19}, f_{20} = Polygon(H_3, G_3, F_3, S_2, T_2)
poly31, g_{20}, h_{20}, i_{20}, j_{20}, k_{20} = Polygon(H_3, T_2, U_2, V_2, I_3)
F_6 = dual_face(J_2, N_1, O_1)
poly32, l_{20}, m_{20}, n_{20}, p_{20}, q_{20} = Polygon(H_3, I_3, F_6, R_5, N_4)
poly33, r_{20}, s_{20}, t_{20}, a_{20}, b_{20} = Polygon(P_4, R_4, D_5, M_5, N_5)
poly34, c_{20}, d_{20}, o_5, e_{20}, f_{21} = Polygon(P_4, N_5, O_5, Q_5, P_5)
poly35, g_{21}, h_{21}, i_{21}, j_{21}, k_{21} = Polygon(P_4, P_5, R_5, N_4, M_4)
poly36, l_{21}, m_{21}, n_{21}, p_{21}, q_{21} = Polygon(P_4, M_4, E_6, L_4, K_4)
poly37, r_{21}, s_{21}, t_{21}, a_{21}, b_{21} = Polygon(P_4, K_4, J_4, Q_4, R_4)
poly38, c_{21}, d_{21}, e_{21}, f_{22}, g_{22} = Polygon(S_5, Q_5, P_5, R_5, F_6)
poly39, h_{22}, i_{22}, j_{22}, k_{22}, l_{22} = Polygon(S_5, F_6, I_3, V_2, W_2)
poly40, m_{22}, n_{22}, p_{22}, q_{22}, r_{22} = Polygon(S_5, W_2, Z_2, J_3, K_3)
G_6 = dual_face(I_1, E_1, D_1)
poly41, s_{22}, t_{22}, a_{22}, b_{22}, c_{22} = Polygon(S_5, K_3, G_6, U_5, T_5)
H_6 = dual_face(J_1, K_1, M_1)
poly42, d_{22}, e_{22}, f_{23}, g_{23}, h_{23} = Polygon(T_5, H_6, O_5, Q_5, S_5)
poly43, i_{23}, j_{23}, k_{23}, l_{23}, m_{23} = Polygon(N_2, Z_2, W_2, V_2, U_2)
poly44, n_{23}, p_{23}, q_{23}, r_{23}, s_{23} = Polygon(N_2, U_2, T_2, S_2, R_2)
poly45, t_{23}, a_{23}, b_{23}, c_{23}, d_{23} = Polygon(N_2, R_2, Q_2, P_2, O_2)
poly46, e_{23}, f_{24}, g_{24}, h_{24}, i_{24} = Polygon(N_2, O_2, M_2, B_3, A_3)
poly47, j_{24}, k_{24}, l_{24}, m_{24}, n_{24} = Polygon(N_2, A_3, C_6, J_3, Z_2)
poly48, p_{24}, q_{24}, r_{24}, s_{24}, t_{24} = Polygon(L_5, M_5, N_5, O_5, H_6)
poly49, a_{24}, b_{24}, c_{24}, d_{24}, e_{24} = Polygon(L_5, H_6, T_5, U_5, B_6)
I_6 = dual_face(G, K, J)
poly50, f_{25}, g_{25}, h_{25}, i_{25}, j_{25} = Polygon(L_5, B_6, A_6, I_6, K_5)
poly51, k_{25}, l_{25}, m_{25}, n_{25}, p_{25} = Polygon(L_5, K_5, J_5, G_5, F_5)
poly52, q_{25}, r_{25}, s_{25}, t_{25}, a_{25} = Polygon(L_5, F_5, E_5, D_5, M_5)
poly53, b_{25}, c_{25}, d_{25}, e_{25}, f_{26} = Polygon(Z_4, I_5, H_5, G_5, J_5)
poly54, g_{26}, h_{26}, i_{26}, j_{26}, k_{26} = Polygon(Z_4, J_5, K_5, I_6, V_5)
poly55, l_{26}, m_{26}, n_{26}, p_{26}, q_{26} = Polygon(Z_4, V_5, W_5, N_3, O_3)
poly56, r_{26}, s_{26}, t_{26}, a_{26}, b_{26} = Polygon(Z_4, O_3, P_3, Q_3, A_5)
poly57, c_{26}, d_{26}, e_{26}, f_{27}, g_{27} = Polygon(Z_4, A_5, B_5, C_5, I_5)
poly58, h_{27}, i_{27}, j_{27}, k_{27}, l_{27} = Polygon(L_3, A_6, B_6, U_5, G_6)
poly59, m_{27}, n_{27}, p_{27}, q_{27}, r_{27} = Polygon(L_3, G_6, K_3, J_3, C_6)
poly60, s_{27}, t_{27}, a_{27}, b_{27}, c_{27} = Polygon(L_3, C_6, A_3, B_3, Z_5)
poly61, d_{27}, e_{27}, f_{28}, g_{28}, h_{28} = Polygon(L_3, Z_5, M_3, N_3, W_5)
poly62, i_{28}, j_{28}, k_{28}, l_{28}, m_{28} = Polygon(L_3, W_5, V_5, I_6, A_6)
poly63, n_{28}, p_{28}, q_{28}, r_{28}, s_{28} = Polygon(U_3, R_3, W_4, Q_3, P_3)
poly64, t_{28}, a_{28}, b_{28}, c_{28}, d_{28} = Polygon(U_3, P_3, O_3, N_3, M_3)
poly65, e_{28}, f_{29}, g_{29}, h_{29}, i_{29} = Polygon(U_3, M_3, Z_5, B_3, M_2)
poly66, j_{29}, k_{29}, l_{29}, m_{29}, n_{29} = Polygon(U_3, M_2, O_2, P_2, C_3)
poly67, p_{29}, q_{29}, r_{29}, s_{29}, t_{29} = Polygon(U_3, C_3, D_3, S_3, R_3)
poly68, a_{29}, b_{29}, c_{29}, d_{29}, e_{29} = Polygon(U_4, E_4, F_4, G_4, D_6)
poly69, f_{30}, g_{30}, h_{30}, i_{30}, j_{30} = Polygon(U_4, D_6, T_4, C_5, B_5)
poly70, k_{30}, l_{30}, m_{30}, n_{30}, p_{30} = Polygon(U_4, B_5, A_5, Q_3, W_4)
poly71, q_{30}, r_{30}, s_{30}, t_{30}, a_{30} = Polygon(U_4, W_4, R_3, S_3, V_4)
poly72, b_{30}, c_{30}, d_{30}, e_{30}, f_{31} = Polygon(U_4, V_4, T_3, D_4, E_4)

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})