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

valider

valider

valider

S =

F =

A =

a: 2
d: ((1 + (2 * sqrt(2))) * a / 2)
c: ((1 + sqrt(2)) * a / 2)
b: a / 2
sommets: 14
faces: 24
aretes: 36
rep1: 0
rep2: 0
rep3: 0
ChampTexte1 = Textfield(rep1)
ChampTexte2 = Textfield(rep2)
ChampTexte3 = Textfield(rep3)
l2 = Sequence(Sequence[Sequence[((c * (-1)^(k)), (b * (-1)^(j)), (c * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l3 = Sequence(Sequence[Sequence[((c * (-1)^(j)), (c * (-1)^(k)), (b * (-1)^(i))), k, 1, 2], j, 1, 2], i, 1, 2)
l1 = Sequence(Sequence[Sequence[((b * (-1)^(i)), (c * (-1)^(j)), (c * (-1)^(k))), k, 1, 2], j, 1, 2], i, 1, 2)
A = Point(l1)
B = Point(l1)
C = Point(l1)
D = Point(l1)
Q = Point(l3)
R = Point(l3)
S = Point(l3)
T = Point(l3)
W = Point(l2)
A_1 = Point(l2)
B_1 = Point(l2)
E_1 = Point(l2)
I_1 = Point(l2)
K_1 = Point(l2)
L_1 = Point(l2)
O_1 = Point(l2)
Q_1 = Point(l3)
S_1 = Point(l3)
A_2 = Point(l3)
C_2 = Point(l3)
F_2 = Point(l1)
J_2 = Point(l1)
K_2 = Point(l1)
L_2 = Point(l1)
E = dual_face(C, S, Q_1)
F = dual_face(D, T, W)
G = dual_face(S_1, L_2, A_1)
H = dual_face(W, T, S_1)
I = dual_face(L_1, C, D)
J = dual_face(L_1, S, C)
K = dual_face(Q_1, J_2, O_1)
L = dual_face(K_1, C_2, K_2)
M = dual_face(R, B, I_1)
N = dual_face(I_1, R, C_2)
O = dual_face(K_2, K_1, O_1)
P = dual_face(Q, A_2, F_2)
U = dual_face(F_2, E_1, A_2)
V = dual_face(Q, A, B_1)
t9, f_4, i_4, e_3 = Polygon(I, E, F)
t10, e_4, i_5, j_4 = Polygon(I, J, E)
t11, h_4, i_6, f_5 = Polygon(I, F, H)
t12, h_5, i_7, v = Polygon(I, V, H)
t13, p_3, i_8, v_1 = Polygon(I, V, P)
t14, m_3, i_9, p_4 = Polygon(I, P, M)
t15, n_3, i_{10}, m_4 = Polygon(I, M, N)
t16, j_5, i_{11}, n_4 = Polygon(I, N, J)
t17, n_5, m_5, p_5 = Polygon(M, P, N)
t18, n_6, p_6, l_4 = Polygon(P, L, N)
t19, o, n_7, l_5 = Polygon(N, L, O)
t20, p_7, l_6, o_2 = Polygon(L, O, P)
t21, e_5, j_6, n_8 = Polygon(J, N, E)
t22, e_6, n_9, k_4 = Polygon(N, K, E)
t23, o_3, n_{10}, k_5 = Polygon(N, K, O)
t24, k_6, e_7, o_4 = Polygon(E, O, K)
t25, h_6, e_8, f_6 = Polygon(E, F, H)
t26, h_7, e_9, g_4 = Polygon(E, G, H)
t27, g_5, e_{10}, o_5 = Polygon(E, O, G)
t28, o_6, h_8, g_6 = Polygon(H, G, O)
t29, o_7, h_9, u = Polygon(H, U, O)
t30, o_8, p_8, u_1 = Polygon(P, U, O)
t31, h_{10}, p_9, u_2 = Polygon(P, U, H)
t32, h_{11}, p_{10}, v_2 = Polygon(P, V, H)

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})