Icosaedro truncado

Cortamos los doce  vértices del icosaedro con planos perpendiculares a las diagonales espaciales.
Casos particulares: icosidodecaedro, icosaedro truncado.

Arista

Radio

Icosaedro truncado

Icosidodecaedro

icosaedro

Secuencia de la animación

Detener la animación en:

t1 = 0.333 (slider from 0 to 0.5, step 1.0E-4)
O: (0, 0, 0)
L = 2.4 (slider from 1 to 4, step 0.1)
n = 3 (slider from 3 to 5, step 1)
c = 1.4142135623730951
t = 1.7320508075688772 (slider from -5 to 5, step 1)
p = 1.1755705045849463
ar = If(n ≟ 3, L / t, If[n ≟ 4, L / c, If[n ≟ 5, L / p]])
RA = 1 (slider from 0 to 1, step 1)
des = If(RA ≟ 0, L, If[RA ≟ 1, ar])
ci = Circle(O, des, xOyPlane)
A = Point(ci)
A' = Rotate(A, (360 * ° / n), O)
A'' = Rotate(A', (360 * ° / n), O)
v = 0.3 (slider from -1 to 1, step 0.1)
b = Distance(A, A')
arista = Distance(A, A')
radio = Distance(O, A'')
P20, B, C, D, E, F, G, H, I, J, caraAA'A'', caraAA''D, caraADE, caraABE, caraAA'B, caraA'BF, caraA'CF, caraA'A''C, caraA''CG, caraA''DG, caraCFI, caraCGI, caraGIJ, caraDGJ, caraFHI, caraHIJ, caraEHJ, caraDEJ, caraBFH, caraBEH, aristaAA'', aristaAA', aristaA'A'', aristaAD, aristaA''D, aristaAE, aristaDE, aristaAB, aristaBE, aristaA'B, aristaA'F, aristaBF, aristaA'C, aristaCF, aristaA''C, aristaA''G, aristaCG, aristaDG, aristaCI, aristaFI, aristaGI, aristaGJ, aristaIJ, aristaDJ, aristaHI, aristaFH, aristaHJ, aristaEJ, aristaEH, aristaBH = Icosahedron(A, A', A'')
i = 4 (slider from 1 to 4, step 1)
K = Midpoint(A, I)
P0: A + ((A' - A) * t1)
a = Sphere(K, P0)
M, N = Intersect(aristaBH, a)
P, Q = Intersect(aristaBE, a)
R, S = Intersect(aristaAB, a)
T, U = Intersect(aristaA'B, a)
V, W = Intersect(aristaA''G, a)
Z, A_1 = Intersect(aristaFH, caraFHI)
B_1, C_1 = Intersect(aristaFH, a)
D_1, E_1 = Intersect(aristaBF, a)
F_1, G_1 = Intersect(aristaA'F, a)
H_1, I_1 = Intersect(aristaFI, a)
J_1, K_1 = Intersect(aristaHI, a)
L_1, M_1 = Intersect(aristaEH, a)
N_1, O_1 = Intersect(aristaCF, a)
P_1, Q_1 = Intersect(aristaHJ, a)
R_1, S_1 = Intersect(aristaEJ, a)
T_1, U_1 = Intersect(aristaDE, a)
V_1, W_1 = Intersect(aristaDJ, a)
Z_1, A_2 = Intersect(aristaAE, a)
B_2, C_2 = Intersect(aristaAD, a)
D_2, E_2 = Intersect(aristaDG, a)
F_2, G_2 = Intersect(aristaGJ, a)
H_2, I_2 = Intersect(aristaA''D, a)
J_2, K_2 = Intersect(aristaAA'', a)
L_2, M_2 = Intersect(aristaA'A'', a)
N_2, O_2 = Intersect(aristaA''C, a)
P_2, Q_2 = Intersect(aristaGI, a)
R_2, S_2 = Intersect(aristaCI, a)
T_2, U_2 = Intersect(aristaIJ, a)
V_2, W_2 = Intersect(aristaCG, a)
Z_2, A_3 = Intersect(aristaA'C, a)
polígono1, d_1, e_1, b_1, c_1, n_1, m = Polygon(D_1, E_1, B_1, C_1, N, M)
polígono2, d_2, t_1, u, g_1, f_1, e_2 = Polygon(D_1, T, U, G_1, F_1, E_1)
polígono3, b_2, h_1, i_1, k_1, j_1, c_2 = Polygon(B_1, H_1, I_1, K_1, J_1, C_1)
polígono4, m_1, n_2, l_1, m_2, p_1, q = Polygon(M, N, L_1, M_1, P, Q)
polígono5, q_1, p_2, z_1, a_2, s, r = Polygon(Q, P, Z_1, A_2, S, R)
B_3, C_3 = Intersect(aristaAA', a)
polígono7, m_3, l_2, p_3, q_2, s_2, r_2 = Polygon(M_1, L_1, P_1, Q_1, S_1, R_1)
polígono8, c_4, a_1, z_2, u_1, t_3, b_4 = Polygon(C_2, A_2, Z_1, U_1, T_1, B_2)
polígono9, t_4, u_2, r_3, s_3, v_1, w_1 = Polygon(T_1, U_1, R_1, S_1, V_1, W_1)
polígono10, e_3, w_2, v_2, f_2, g_2, d_3 = Polygon(E_2, W_1, V_1, F_2, G_2, D_2)
polígono11, h_2, i_2, e_4, d_4, v_3, w = Polygon(H_2, I_2, E_2, D_2, V, W)
polígono12, o_2, w_3, v_4, w_4, v_5, n_3 = Polygon(O_2, W, V, W_2, V_2, N_2)
polígono13, g_3, f_3, u_3, t_5, p_4, q_3 = Polygon(G_2, F_2, U_2, T_2, P_2, Q_2)
polígono14, v_6, w_5, q_4, p_5, r_4, s_4 = Polygon(V_2, W_2, Q_2, P_2, R_2, S_2)
polígono15, n_4, o_1, s_5, r_5, i_3, h_3 = Polygon(N_1, O_1, S_2, R_2, I_1, H_1)
polígono16, a_3, z_3, o_3, n_5, f_4, g_4 = Polygon(A_3, Z_2, O_1, N_1, F_1, G_1)
polígono18, b_6, i_4, h_4, j_2, k_2, c_5 = Polygon(B_2, I_2, H_2, J_2, K_2, C_2)
polígono19, m_4, o_4, n_6, z_5, a_4, l_4 = Polygon(M_2, O_2, N_2, Z_2, A_3, L_2)
polígono20, b_7, c_6, u_5, t_7, r_6, s_7 = Polygon(B_3, C_3, U, T, R, S)
polígono21, t_8, u_6, q_5, p_6, j_3, k_3 = Polygon(T_2, U_2, Q_1, P_1, J_1, K_1)
polígono6, m_5, l_3, c_3, b_3, k_4, j_4 = Polygon(M_2, L_2, C_3, B_3, K_2, J_2)
polígono17, i_5, b_5, t_2, w_6, e_5 = Polygon(I_2, B_2, T_1, W_1, E_2)
polígono22, v_7, s_1, q_6, u_4, f_5 = Polygon(V_1, S_1, Q_1, U_2, F_2)
polígono23, u_7, z_4, p_7, m_6, r_1 = Polygon(U_1, Z_1, P, M_1, R_1)
polígono24, k_5, b_8, s_6, a_5, c_7 = Polygon(K_2, B_3, S, A_2, C_2)
D_3 = Intersect(o_2, m_4)
polígono25, m_7, j_5, h_5, w_7, d_5 = Polygon(M_2, J_2, H_2, W, D_3)
polígono26, v_8, d_6, g_5, q_7, w_8 = Polygon(V, D_2, G_2, Q_2, W_2)
polígono27, r_7, p_8, t_6, k_6, i_6 = Polygon(R_2, P_2, T_2, K_1, I_1)
polígono28, o_5, z_6, n_7, v_9, s_8 = Polygon(O_1, Z_2, N_2, V_2, S_2)
polígono29, f_6, n_8, h_6, b_9, e_6 = Polygon(F_1, N_1, H_1, B_1, E_1)
polígono30, r_8, t_9, d_7, m_8, q_8 = Polygon(R, T, D_1, M, Q)
polígono31, c_8, l_5, a_6, g_6, u_8 = Polygon(C_3, L_2, A_3, G_1, U)
polígono32, l_6, n_9, c_9, j_6, p_9 = Polygon(L_1, N, C_1, J_1, P_1)
distanciaS1V1 = Distance(S_1, V_1)
distanciaV1W1 = Distance(V_1, W_1)
vel = 0 (slider from 0 to 1, step 0.1)
v10: (10 * v)
texto1: "Arista del icosaedro " + L + ""
texto2: "Velocidad de giro " + v10 + ""
vel10: (10 * vel)
texto3: "Velocidad del corte " + vel10 + ""