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

valider

valider

valider

S =

F =

A =

t: (1 + (19 + (3 * sqrt(33)))^(1 / 3) + (19 - (3 * sqrt(33)))^(1 / 3)) / 3
u: 1 / t
a: 1.5
sommets: 38
faces: 24
aretes: 60
rep1: 0
rep2: 0
rep3: 0
ChampTexte1 = Textfield(rep1)
ChampTexte2 = Textfield(rep2)
ChampTexte3 = Textfield(rep3)
b: (a * t)
c: (a * u)
A: ((-a), (-b), (-c))
B: ((-c), (-a), (-b))
C: ((-b), (-c), (-a))
D: (a, b, (-c))
E: (a, (-b), c)
F: ((-a), b, c)
G: (c, a, (-b))
H: (c, (-a), b)
I: ((-c), a, b)
J: (b, c, (-a))
K: (b, (-c), a)
L: ((-b), c, a)
M: (b, a, c)
N: (c, b, a)
O: (a, c, b)
P: (b, (-a), (-c))
Q: ((-b), a, (-c))
R: ((-b), (-a), c)
S: (c, (-b), (-a))
T: ((-c), b, (-a))
U: ((-c), (-b), a)
V: (a, (-c), (-b))
W: ((-a), (-c), b)
Z: ((-a), c, (-b))
A1: (0, 0, 0)
p_5 = Plane(W, H, A1)
A_1 = point_dual(I, W, H, A1)
B_1 = point_dual(W, U, H, A1)
C_1 = point_dual(H, U, E, A1)
D_1 = point_dual(H, E, K, A1)
E_1 = point_dual(O, H, K, A1)
poly1, f_5, g_5, h_5, i_5, j_5 = Polygon(A_1, B_1, C_1, D_1, E_1)
F_1 = point_dual(W, R, U, A1)
G_1 = point_dual(W, L, R, A1)
H_1 = point_dual(I, L, W, A1)
I_1 = point_dual(I, F, L, A1)
J_1 = point_dual(F, Q, L, A1)
K_1 = point_dual(L, Q, C, A1)
L_1 = point_dual(R, C, A, A1)
M_1 = point_dual(U, R, A, A1)
N_1 = point_dual(Q, C, Z, A1)
O_1 = point_dual(C, Z, B, A1)
P_1 = point_dual(C, B, A, A1)
Q_1 = point_dual(Q, Z, T, A1)
R_1 = point_dual(F, T, Q, A1)
S_1 = point_dual(N, F, I, A1)
T_1 = point_dual(O, M, K, A1)
U_1 = point_dual(K, P, E, A1)
V_1 = point_dual(S, P, E, A1)
W_1 = point_dual(O, M, N, A1)
Z_1 = point_dual(I, O, N, A1)
A_2 = point_dual(K, P, J, A1)
B_2 = point_dual(M, J, D, A1)
C_2 = point_dual(N, M, D, A1)
D_2 = point_dual(P, V, J, A1)
E_2 = point_dual(J, V, G, A1)
F_2 = point_dual(J, G, D, A1)
G_2 = point_dual(S, V, P, A1)
H_2 = point_dual(D, G, T, A1)
I_2 = point_dual(N, D, T, A1)
J_2 = point_dual(G, V, B, A1)
K_2 = point_dual(T, G, Z, I_2)
L_2 = point_dual(T, G, Z, A1)
M_2 = point_dual(U, E, S, A1)
N_2 = point_dual(S, B, A, A1)
O_2 = point_dual(S, B, V, A1)
poly2, k_5, l_5, m_5, n_5, q_5 = Polygon(A_1, H_1, G_1, F_1, B_1)
poly3, r_5, s_5, d_5, e_5, f_6 = Polygon(A_1, H_1, I_1, S_1, Z_1)
poly4, g_6, h_6, i_6, j_6, k_6 = Polygon(A_1, Z_1, W_1, T_1, E_1)
poly5, l_6, m_6, n_6, p_6, q_6 = Polygon(K_1, J_1, I_1, H_1, G_1)
poly6, r_6, s_6, t_6, a_6, b_6 = Polygon(K_1, G_1, F_1, M_1, L_1)
poly7, c_6, d_6, e_6, f_7, g_7 = Polygon(K_1, L_1, P_1, O_1, N_1)
poly8, h_7, i_7, j_7, k_7, l_7 = Polygon(K_1, N_1, Q_1, R_1, J_1)
poly9, m_7, n_7, p_7, q_7, r_7 = Polygon(I_2, H_2, L_2, Q_1, R_1)
poly10, s_7, t_7, a_7, b_7, c_7 = Polygon(I_2, R_1, J_1, I_1, S_1)
poly11, d_7, e_7, f_8, g_8, h_8 = Polygon(I_2, S_1, Z_1, W_1, C_2)
poly12, i_8, j_8, k_8, l_8, m_8 = Polygon(I_2, C_2, B_2, F_2, H_2)
poly13, n_8, p_8, q_8, r_8, s_8 = Polygon(A_2, B_2, C_2, W_1, T_1)
poly14, t_8, a_8, b_8, c_8, d_8 = Polygon(A_2, T_1, E_1, D_1, U_1)
poly15, e_8, f_9, g_9, h_9, i_9 = Polygon(A_2, U_1, V_1, G_2, D_2)
poly16, j_9, k_9, l_9, m_9, n_9 = Polygon(A_2, D_2, E_2, F_2, B_2)
poly17, p_9, q_9, r_9, s_9, t_9 = Polygon(J_2, E_2, D_2, G_2, O_2)
poly18, a_9, b_9, c_9, d_9, e_9 = Polygon(J_2, E_2, F_2, H_2, L_2)
poly19, f_{10}, g_{10}, h_{10}, i_{10}, j_{10} = Polygon(J_2, O_2, N_2, P_1, O_1)
poly20, k_{10}, l_{10}, m_{10}, n_{10}, p_{10} = Polygon(J_2, O_1, N_1, Q_1, L_2)
poly21, q_{10}, r_{10}, s_{10}, t_{10}, a_{10} = Polygon(M_2, V_1, U_1, D_1, C_1)
poly22, b_{10}, c_{10}, d_{10}, e_{10}, f_{11} = Polygon(M_2, C_1, B_1, F_1, M_1)
poly23, g_{11}, h_{11}, i_{11}, j_{11}, k_{11} = Polygon(M_2, M_1, L_1, P_1, N_2)
poly24, l_{11}, m_{11}, n_{11}, p_{11}, q_{11} = Polygon(M_2, N_2, O_2, G_2, V_1)

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: perp_espace (command perp_espace1)
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)