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

valider

valider

valider

S =

F =

A =

a = 2
b: a / sqrt(2)
A: (b, (2 * b), 0)
B: (b, (-2 * b), 0)
C: ((-b), (2 * b), 0)
D: ((-b), (-2 * b), 0)
E: (0, b, (2 * b))
F: (0, b, (-2 * b))
G: (0, (-b), (2 * b))
H: (0, (-b), (-2 * b))
I: (b, 0, (2 * b))
J: (b, 0, (-2 * b))
K: ((-b), 0, (2 * b))
L: ((-b), 0, (-2 * b))
N: ((2 * b), 0, (-b))
O: ((-2 * b), 0, b)
P: ((-2 * b), 0, (-b))
Q: ((2 * b), b, 0)
R: ((2 * b), (-b), 0)
S: ((-2 * b), b, 0)
T: ((-2 * b), (-b), 0)
U: (0, (2 * b), b)
V: (0, (2 * b), (-b))
W: (0, (-2 * b), b)
Z: (0, (-2 * b), (-b))
M: ((2 * b), 0, b)
sommets: 14
faces: 24
aretes: 36
rep1: 0
rep2: 0
rep3: 0
ChampTexte1 = Textfield(rep1)
ChampTexte2 = Textfield(rep2)
ChampTexte3 = Textfield(rep3)
A_1 = dual_face(G, I, M)
B_1 = dual_face(I, M, Q)
C_1 = dual_face(Q, N, R)
D_1 = dual_face(B, R, N)
E_1 = dual_face(N, Q, A)
F_1 = dual_face(E, I, G)
G_1 = dual_face(W, D, Z)
H_1 = dual_face(Z, H, L)
I_1 = dual_face(P, S, O)
J_1 = dual_face(O, K, E)
K_1 = dual_face(K, O, T)
L_1 = dual_face(C, V, F)
M_1 = dual_face(C, U, A)
N_1 = dual_face(J, F, L)
t1, f_3, g_3, h_3 = Polygon(F_1, B_1, J_1)
t2, i_3, j_3, k_3 = Polygon(F_1, B_1, A_1)
t3, l_3, m_3, n_3 = Polygon(F_1, A_1, K_1)
t4, p_3, q_3, r_3 = Polygon(F_1, K_1, J_1)
t5, s_3, t_3, c_3 = Polygon(C_1, B_1, A_1)
t6, d_3, e_3, f_4 = Polygon(B_1, M_1, J_1)
t9, m_4, n_4, p_4 = Polygon(M_1, E_1, L_1)
t10, q_4, r_4, s_4 = Polygon(J_1, I_1, K_1)
t11, t_4, a_4, b_4 = Polygon(J_1, L_1, M_1)
t12, c_4, d_4, e_4 = Polygon(J_1, L_1, I_1)
t13, f_5, g_5, h_5 = Polygon(I_1, L_1, H_1)
t14, i_5, j_5, k_5 = Polygon(I_1, K_1, H_1)
t15, l_5, m_5, n_5 = Polygon(K_1, G_1, H_1)
t16, p_5, q_5, r_5 = Polygon(K_1, G_1, A_1)
t17, s_5, t_5, a_5 = Polygon(G_1, H_1, D_1)
t18, b_5, c_5, d_5 = Polygon(G_1, A_1, D_1)
t7, g_4, h_4, i_4 = Polygon(B_1, M_1, E_1)
t8, j_4, k_4, l_4 = Polygon(B_1, E_1, C_1)
t19, e_5, f_6, g_6 = Polygon(C_1, D_1, E_1)
t20, h_6, i_6, j_6 = Polygon(C_1, D_1, A_1)
t21, k_6, l_6, m_6 = Polygon(N_1, H_1, L_1)
t22, n_6, p_6, q_6 = Polygon(N_1, E_1, L_1)
t23, r_6, s_6, t_6 = Polygon(N_1, E_1, D_1)
t24, a_6, b_6, c_6 = Polygon(N_1, D_1, H_1)

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})