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

valider

valider

valider

S =

F =

A =

A1 = 0.500000000000001
B1 = 0
C1 = 2.42705098312484
A2 = 0.500000000000001
B2 = 0
C2 = -2.42705098312484
A3 = -0.500000000000001
B3 = 0
C3 = 2.42705098312484
A4 = -0.500000000000001
B4 = 0
C4 = -2.42705098312484
A5 = 2.42705098312484
B5 = 0.500000000000001
C5 = 0
A6 = 2.42705098312484
B6 = -0.500000000000001
C6 = 0
A7 = -2.42705098312484
B7 = 0.500000000000001
C7 = 0
A8 = -2.42705098312484
B8 = -0.500000000000001
C8 = 0
A9 = 0
B9 = 2.42705098312484
C9 = 0.500000000000001
A10 = 0
B10 = 2.42705098312484
C10 = -0.500000000000001
A11 = 0
B11 = -2.42705098312484
C11 = 0.500000000000001
A12 = 0
B12 = -2.42705098312484
C12 = -0.500000000000001
A13 = 1
B13 = 0.809016994374948
C13 = 2.1180339887499
A14 = 1
B14 = 0.809016994374948
C14 = -2.1180339887499
A15 = 1
B15 = -0.809016994374948
C15 = 2.1180339887499
A16 = 1
B16 = -0.809016994374948
C16 = -2.1180339887499
A17 = -1
B17 = 0.809016994374948
C17 = 2.1180339887499
A18 = -1
B18 = 0.809016994374948
C18 = -2.1180339887499
A19 = -1
B19 = -0.809016994374948
C19 = 2.1180339887499
A20 = -1
B20 = -0.809016994374948
C20 = -2.1180339887499
A21 = 2.1180339887499
B21 = 1
C21 = 0.809016994374948
A22 = 2.1180339887499
B22 = 1
C22 = -0.809016994374948
A23 = 2.1180339887499
B23 = -1
C23 = 0.809016994374948
A24 = 2.1180339887499
B24 = -1
C24 = -0.809016994374948
A25 = -2.1180339887499
B25 = 1
C25 = 0.809016994374948
A26 = -2.1180339887499
B26 = 1
C26 = -0.809016994374948
A27 = -2.1180339887499
B27 = -1
C27 = 0.809016994374948
A28 = -2.1180339887499
B28 = -1
C28 = -0.809016994374948
A29 = 0.809016994374948
B29 = 2.1180339887499
C29 = 1
A30 = 0.809016994374948
B30 = 2.1180339887499
C30 = -1
A31 = 0.809016994374948
B31 = -2.1180339887499
C31 = 1
A32 = 0.809016994374948
B32 = -2.1180339887499
C32 = -1
A33 = -0.809016994374948
B33 = 2.1180339887499
C33 = 1
A34 = -0.809016994374948
B34 = 2.1180339887499
C34 = -1
A35 = -0.809016994374948
B35 = -2.1180339887499
C35 = 1
A36 = -0.809016994374948
B36 = -2.1180339887499
C36 = -1
A37 = 0.500000000000001
B37 = 1.6180339887499
C37 = 1.80901699437495
A38 = 0.500000000000001
B38 = 1.6180339887499
C38 = -1.80901699437495
A39 = 0.500000000000001
B39 = -1.6180339887499
C39 = 1.80901699437495
A40 = 0.500000000000001
B40 = -1.6180339887499
C40 = -1.80901699437495
A41 = -0.500000000000001
B41 = 1.6180339887499
C41 = 1.80901699437495
A42 = -0.500000000000001
B42 = 1.6180339887499
C42 = -1.80901699437495
A43 = -0.500000000000001
B43 = -1.6180339887499
C43 = 1.80901699437495
A44 = -0.500000000000001
B44 = -1.6180339887499
C44 = -1.80901699437495
A45 = 1.80901699437495
B45 = 0.500000000000001
C45 = 1.6180339887499
A46 = 1.80901699437495
B46 = 0.500000000000001
C46 = -1.6180339887499
A47 = 1.80901699437495
B47 = -0.500000000000001
C47 = 1.6180339887499
A48 = 1.80901699437495
B48 = -0.500000000000001
C48 = -1.6180339887499
A49 = -1.80901699437495
B49 = 0.500000000000001
C49 = 1.6180339887499
A50 = -1.80901699437495
B50 = 0.500000000000001
C50 = -1.6180339887499
A51 = -1.80901699437495
B51 = -0.500000000000001
C51 = 1.6180339887499
A52 = -1.80901699437495
B52 = -0.500000000000001
C52 = -1.6180339887499
A53 = 1.6180339887499
B53 = 1.80901699437495
C53 = 0.500000000000001
A54 = 1.6180339887499
B54 = 1.80901699437495
C54 = -0.500000000000001
A55 = 1.6180339887499
B55 = -1.80901699437495
C55 = 0.500000000000001
A56 = 1.6180339887499
B56 = -1.80901699437495
C56 = -0.500000000000001
A57 = -1.6180339887499
B57 = 1.80901699437495
C57 = 0.500000000000001
A58 = -1.6180339887499
B58 = 1.80901699437495
C58 = -0.500000000000001
A59 = -1.6180339887499
B59 = -1.80901699437495
C59 = 0.500000000000001
A60 = -1.6180339887499
B60 = -1.80901699437495
C60 = -0.500000000000001
A62 = 1
B62 = 15
C62 = 47
D62 = 45
E62 = 13
A63 = 2
B63 = 14
C63 = 46
D63 = 48
E63 = 16
A64 = 3
B64 = 17
C64 = 49
D64 = 51
E64 = 19
A65 = 4
B65 = 20
C65 = 52
D65 = 50
E65 = 18
A66 = 5
B66 = 22
C66 = 54
D66 = 53
E66 = 21
A67 = 6
B67 = 23
C67 = 55
D67 = 56
E67 = 24
A68 = 7
B68 = 25
C68 = 57
D68 = 58
E68 = 26
A69 = 8
B69 = 28
C69 = 60
D69 = 59
E69 = 27
A70 = 9
B70 = 33
C70 = 41
D70 = 37
E70 = 29
A71 = 10
B71 = 30
C71 = 38
D71 = 42
E71 = 34
A72 = 11
B72 = 31
C72 = 39
D72 = 43
E72 = 35
A73 = 12
B73 = 36
C73 = 44
D73 = 40
E73 = 32
A74 = 1
B74 = 3
C74 = 19
D74 = 43
E74 = 39
F74 = 15
A75 = 1
B75 = 13
C75 = 37
D75 = 41
E75 = 17
F75 = 3
A76 = 2
B76 = 4
C76 = 18
D76 = 42
E76 = 38
F76 = 14
A77 = 2
B77 = 16
C77 = 40
D77 = 44
E77 = 20
F77 = 4
A78 = 21
B78 = 45
C78 = 47
D78 = 23
E78 = 6
F78 = 5
A79 = 21
B79 = 53
C79 = 29
D79 = 37
E79 = 13
F79 = 45
A80 = 24
B80 = 48
C80 = 46
D80 = 22
E80 = 5
F80 = 6
A81 = 24
B81 = 56
C81 = 32
D81 = 40
E81 = 16
F81 = 48
A82 = 25
B82 = 49
C82 = 17
D82 = 41
E82 = 33
F82 = 57
A83 = 25
B83 = 7
C83 = 8
D83 = 27
E83 = 51
F83 = 49
A84 = 28
B84 = 52
C84 = 20
D84 = 44
E84 = 36
F84 = 60
A85 = 28
B85 = 8
C85 = 7
D85 = 26
E85 = 50
F85 = 52
A86 = 30
B86 = 54
C86 = 22
D86 = 46
E86 = 14
F86 = 38
A87 = 30
B87 = 10
C87 = 9
D87 = 29
E87 = 53
F87 = 54
A88 = 31
B88 = 55
C88 = 23
D88 = 47
E88 = 15
F88 = 39
A89 = 31
B89 = 11
C89 = 12
D89 = 32
E89 = 56
F89 = 55
A90 = 34
B90 = 58
C90 = 57
D90 = 33
E90 = 9
F90 = 10
A91 = 34
B91 = 42
C91 = 18
D91 = 50
E91 = 26
F91 = 58
A92 = 35
B92 = 59
C92 = 60
D92 = 36
E92 = 12
F92 = 11
A93 = 35
B93 = 43
C93 = 19
D93 = 51
E93 = 27
F93 = 59
G1: (A1, B1, C1)
G2: (A2, B2, C2)
G3: (A3, B3, C3)
G4: (A4, B4, C4)
G5: (A5, B5, C5)
G6: (A6, B6, C6)
G7: (A7, B7, C7)
G8: (A8, B8, C8)
G9: (A9, B9, C9)
G10: (A10, B10, C10)
G11: (A11, B11, C11)
G12: (A12, B12, C12)
G13: (A13, B13, C13)
G14: (A14, B14, C14)
G15: (A15, B15, C15)
G16: (A16, B16, C16)
G17: (A17, B17, C17)
G18: (A18, B18, C18)
G19: (A19, B19, C19)
G20: (A20, B20, C20)
G21: (A21, B21, C21)
G22: (A22, B22, C22)
G23: (A23, B23, C23)
G24: (A24, B24, C24)
G25: (A25, B25, C25)
G26: (A26, B26, C26)
G27: (A27, B27, C27)
G28: (A28, B28, C28)
G29: (A29, B29, C29)
G30: (A30, B30, C30)
G31: (A31, B31, C31)
G32: (A32, B32, C32)
G33: (A33, B33, C33)
G34: (A34, B34, C34)
G35: (A35, B35, C35)
G36: (A36, B36, C36)
G37: (A37, B37, C37)
G38: (A38, B38, C38)
G39: (A39, B39, C39)
G40: (A40, B40, C40)
G41: (A41, B41, C41)
G42: (A42, B42, C42)
G43: (A43, B43, C43)
G44: (A44, B44, C44)
G45: (A45, B45, C45)
G46: (A46, B46, C46)
G47: (A47, B47, C47)
G48: (A48, B48, C48)
G49: (A49, B49, C49)
G50: (A50, B50, C50)
G51: (A51, B51, C51)
G52: (A52, B52, C52)
G53: (A53, B53, C53)
G54: (A54, B54, C54)
G55: (A55, B55, C55)
G56: (A56, B56, C56)
G57: (A57, B57, C57)
G58: (A58, B58, C58)
G59: (A59, B59, C59)
G60: (A60, B60, C60)
sommets: 32
faces: 60
aretes: 90
rep1: 0
rep2: 0
rep3: 0
ChampTexte1 = Textfield(rep1)
ChampTexte2 = Textfield(rep2)
ChampTexte3 = Textfield(rep3)
A: (0, 0, 0)
B = point_dual(G1, G15, G47, A)
C = point_dual(G39, G31, G55, A)
D = point_dual(G47, G23, G6, A)
E = point_dual(G13, G45, G21, A)
F = point_dual(G23, G55, G56, A)
G = point_dual(G43, G35, G11, A)
H = point_dual(G27, G8, G28, A)
I = point_dual(G12, G36, G44, A)
J = point_dual(G3, G17, G49, A)
K = point_dual(G25, G57, G58, A)
L = point_dual(G41, G37, G29, A)
M = point_dual(G53, G54, G22, A)
N = point_dual(G10, G30, G38, A)
O = point_dual(G46, G48, G16, A)
P = point_dual(G20, G4, G18, A)
Q = point_dual(G29, G53, G54, A)
T = point_dual(G9, G10, G34, A)
U = point_dual(G41, G33, G57, A)
V = point_dual(G1, G13, G37, A)
W = point_dual(G58, G26, G50, A)
Z = point_dual(G7, G26, G50, A)
A_1 = point_dual(G49, G25, G7, A)
B_1 = point_dual(G60, G28, G52, A)
C_1 = point_dual(G59, G60, G36, A)
D_1 = point_dual(G43, G35, G59, A)
E_1 = point_dual(G1, G3, G19, A)
F_1 = point_dual(G55, G56, G32, A)
G_1 = point_dual(G56, G24, G48, A)
H_1 = point_dual(G6, G24, G48, A)
J_1 = point_dual(G16, G2, G4, A)
K_1 = point_dual(G14, G38, G42, A)
L_1 = point_dual(G22, G46, G14, A)
t1, e, v, b = Polygon(V, B, E)
t2, e_1, v_1, b_1 = Polygon(V, B, E_1)
t3, f, v_2, j = Polygon(V, J, E_1)
t4, u, v_3, j_1 = Polygon(V, J, U)
t5, l, v_4, u_1 = Polygon(V, U, L)
t6, e_2, v_5, l_1 = Polygon(V, L, E)
t7, q, e_3, m = Polygon(E, M, Q)
t8, e_4, l_2, q_1 = Polygon(L, Q, E)
t9, q_2, l_3, t = Polygon(L, T, Q)
t10, n, q_3, t_1 = Polygon(Q, T, N)
t11, g, q_4, n_1 = Polygon(Q, N, L_1)
t12, q_5, h, m_1 = Polygon(L_1, M, Q)
t13, l_4, u_2, t_2 = Polygon(U, T, L)
t14, k, u_3, t_3 = Polygon(U, T, K)
t15, w, t_4, k_1 = Polygon(T, K, W)
t16, n_2, t_5, w_1 = Polygon(T, W, N)
t17, u_4, j_2, a_1 = Polygon(J, A_1, U)
t18, u_5, i, k_2 = Polygon(A_1, K, U)
t19, k_3, p, z_1 = Polygon(A_1, Z, K)
t20, z_2, r, h_1 = Polygon(A_1, H, Z)
t21, h_2, s, d_1 = Polygon(A_1, D_1, H)
t22, a, c, j_3 = Polygon(A_1, J, D_1)
t23, c_1, g_1, d = Polygon(G, D_1, C_1)
t24, f_1, g_2, i_1 = Polygon(G, C_1, F_1)
t25, i_2, p_1, r_1 = Polygon(C_1, F_1, I)
t26, s_1, i_3, f_2 = Polygon(I, B_1, C_1)
t27, m_2, h_3, p_2 = Polygon(H, B_1, C_1)
t28, r_2, h_4, s_2 = Polygon(H, C_1, D_1)
t29, j_4, a_2, b_2 = Polygon(E_1, D_1, J)
t30, c_2, d_2, g_3 = Polygon(E_1, G, D_1)
t31, g_4, f_3, c_3 = Polygon(E_1, C, G)
t32, b_3, m_3, c_4 = Polygon(E_1, C, B)
t33, d_3, b_4, c_5 = Polygon(B, C, D)
t34, g_5, c_6, n_3 = Polygon(C, F_1, G)
t35, p_3, c_7, f_4 = Polygon(C, F, F_1)
t36, c_8, d_4, f_5 = Polygon(D, F, C)
t37, e_5, d_5, b_5 = Polygon(D, B, E)
t38, d_6, e_6, m_4 = Polygon(E, M, D)
t39, r_3, d_7, m_5 = Polygon(D, M, H_1)
t40, f_6, d_8, s_3 = Polygon(D, H_1, F)
t41, i_4, a_3, k_4 = Polygon(F_1, G_1, I)
t42, f_7, n_4, p_4 = Polygon(F_1, G_1, F)
t43, r_4, f_8, s_4 = Polygon(F, H_1, G_1)
t44, a_4, i_5, h_5 = Polygon(I, J_1, B_1)
t45, j_5, i_6, k_5 = Polygon(I, G_1, J_1)
t46, l_5, n_5, o = Polygon(G_1, O, J_1)
t47, p_5, o_1, r_5 = Polygon(O, K_1, J_1)
t48, p_6, s_5, a_5 = Polygon(J_1, K_1, P)
t49, g_6, h_6, p_7 = Polygon(B_1, P, J_1)
t50, j_6, h_7, z_3 = Polygon(H, Z, B_1)
t51, k_6, z_4, p_8 = Polygon(Z, P, B_1)
t52, k_7, z_5, w_2 = Polygon(Z, W, K)
t53, z_6, w_3, p_9 = Polygon(W, P, Z)
t54, p_{10}, w_4, l_6 = Polygon(W, K_1, P)
t55, w_5, n_6, m_6 = Polygon(N, K_1, W)
t56, q_6, n_7, r_6 = Polygon(N, K_1, L_1)
t57, s_6, t_6, o_2 = Polygon(K_1, O, L_1)
t58, a_6, m_7, b_6 = Polygon(M, H_1, L_1)
t59, g_7, i_7, o_3 = Polygon(H_1, O, G_1)
t60, o_4, j_7, l_7 = Polygon(H_1, L_1, O)

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)