Dodecaedro truncado

Cortamos los veinte vértices del dodecaedro con planos perpendiculares a las diagonales que unen vértices opuestos.
Casos particulares: icosidodecaedro, dodecaedro truncado.

Arista

Radio

Icosidodecaedro

Dodecaedro truncado

Dodecaedro

Animación

Detener la animación en:

t1 = 0.276 (slider from 0 to 0.5, step 0.001)
O: (0, 0, 0)
L = 2.6 (slider from 1 to 4, step 0.1)
n = 5 (slider from 3 to 5, step 1)
c = 1.4142135623730951
t = 1.7320508075688772
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 = 0.4 (slider from -1 to 1, step 0.1)
b = Distance(A, A')
arista = Distance(A, A')
radio = Distance(O, A'')
P12, B, C, D, E, F, G, H, I, J, K, M, N, P, Q, R, S, T, caraAA'A''BC, caraACGNH, caraAA'DIH, caraA'A''EJD, caraA''BFKE, caraBCGMF, caraGMSTN, caraHIPTN, caraDIPQJ, caraEJQRK, caraFKRSM, caraPQRST, aristaAC, aristaAA', aristaA'A'', aristaA''B, aristaBC, aristaAH, aristaCG, aristaGN, aristaHN, aristaHI, aristaDI, aristaA'D, aristaDJ, aristaEJ, aristaA''E, aristaEK, aristaFK, aristaBF, aristaFM, aristaGM, aristaMS, aristaST, aristaNT, aristaPT, aristaIP, aristaPQ, aristaJQ, aristaQR, aristaKR, aristaRS = Dodecahedron(A, A', A'')
U = Midpoint(A, R)
i = 4 (slider from 1 to 4, step 1)
P0: A + ((A' - A) * t1)
a = Sphere(U, P0)
V, W = Intersect(aristaPT, a)
Z, A_1 = Intersect(aristaPQ, a)
B_1, C_1 = Intersect(aristaDI, a)
D_1, E_1 = Intersect(aristaHI, a)
F_1 = Intersect(aristaCG, aristaJQ)
G_1, H_1 = Intersect(aristaJQ, a)
I_1, J_1 = Intersect(aristaDJ, a)
K_1, L_1 = Intersect(aristaEJ, a)
M_1, N_1 = Intersect(aristaQR, a)
O_1, P_1 = Intersect(aristaRS, a)
Q_1, R_1 = Intersect(aristaEK, a)
S_1, T_1 = Intersect(aristaAC, a)
U_1, V_1 = Intersect(aristaFK, a)
W_1, Z_1 = Intersect(aristaFM, a)
A_2, B_2 = Intersect(aristaMS, a)
C_2, D_2 = Intersect(aristaST, a)
E_2, F_2 = Intersect(aristaGN, a)
G_2, H_2 = Intersect(aristaGM, a)
I_2 = Intersect(aristaBF, aristaBC)
J_2, K_2 = Intersect(aristaBF, a)
L_2, M_2 = Intersect(aristaBC, a)
N_2, O_2 = Intersect(aristaCG, a)
P_2, Q_2 = Intersect(aristaHN, a)
R_2, S_2 = Intersect(aristaAH, a)
T_2, U_2 = Intersect(aristaAA', a)
V_2, W_2 = Intersect(aristaA'D, a)
Z_2, A_3 = Intersect(aristaA'A'', a)
B_3, C_3 = Intersect(aristaA''B, a)
D_3, E_3 = Intersect(aristaA''E, a)
F_3, G_3 = Intersect(aristaKR, a)
H_3, I_3 = Intersect(aristaIP, a)
J_3, K_3 = Intersect(aristaNT, a)
polígono2, p_2, q_2, d_1, e_1, i_3, h_3, w_9, v_1, j_1, k_1 = Polygon(P_2, Q_2, D_1, E_1, I_3, H_3, W, V, J_3, K_3)
polígono3, b_1, c_1, i_1, j_2, h_1, g_1, a_1, z_1, h_4, i_2 = Polygon(B_1, C_1, I_1, J_1, H_1, G_1, A_1, Z, H_3, I_3)
polígono4, m_1, n_1, o_1, p_1, c_3, d_3, v_2, w_1, z_2, a_3 = Polygon(M_1, N_1, O_1, P_1, C_2, D_2, V, W, Z, A_1)
polígono5, m_2, n_2, f_3, g_3, r_1, q_1, l_1, k_2, h_5, g_4 = Polygon(M_1, N_1, F_3, G_3, R_1, Q_1, L_1, K_1, H_1, G_1)
polígono6, f_1, o_2, p_3, b_3, a_4, z_3, w_2, v_3, u_1, g_5 = Polygon(F_3, O_1, P_1, B_2, A_2, Z_1, W_1, V_1, U_1, G_3)
polígono7, e_3, f_4, p_4, q_3, r_2, s_2, t_1, s_1, n_3, o_3 = Polygon(E_2, F_2, P_2, Q_2, R_2, S_2, T_1, S_1, N_2, O_2)
polígono8, l_2, m_3, n_4, o_4, h_6, g_6, z_4, w_3, j_4, k_4 = Polygon(L_2, M_2, N_2, O_2, H_2, G_2, Z_1, W_1, J_2, K_2)
polígono9, b_4, c_4, k_5, j_5, v_4, u_2, r_3, q_4, d_4, e_4 = Polygon(B_3, C_3, K_2, J_2, V_1, U_1, R_1, Q_1, D_3, E_3)
polígono10, z_5, a_5, e_5, d_5, l_3, k_6, j_6, i_4, v_5, w_4 = Polygon(Z_2, A_3, E_3, D_3, L_1, K_1, J_1, I_1, V_2, W_2)
polígono11, s_3, t_2, u_3, w_5, v_6, c_5, b_5, e_6, d_6, r_4 = Polygon(S_2, T_2, U_2, W_2, V_2, C_1, B_1, E_1, D_1, R_2)
polígono12, t_3, u_4, z_6, a_6, b_6, c_6, l_4, m_4, s_4, t_4 = Polygon(T_2, U_2, Z_2, A_3, B_3, C_3, L_2, M_2, S_1, T_1)
polígono13, a_7, g_7, h_7, e_7, f_5, k_7, j_7, d_7, c_7, b_7 = Polygon(A_2, G_2, H_2, E_2, F_2, K_3, J_3, D_2, C_2, B_2)
t1_1, h_2, z_7, w_6 = Polygon(Z, W, H_3)
t2, g_2, m_5, a_2 = Polygon(M_1, A_1, G_1)
t3, f_2, n_5, o_5 = Polygon(N_1, O_1, F_3)
t4, b_2, p_5, c_2 = Polygon(P_1, C_2, B_2)
t5, d_2, j_3, v_7 = Polygon(J_3, V, D_2)
t6, f_6, p_6, k_3 = Polygon(P_2, K_3, F_2)
t7, l_5, d_8, q_5 = Polygon(D_3, Q_1, L_1)
t8, r_5, q_6, d_9 = Polygon(Q_2, D_1, R_2)
t9, i_5, e_2, b_8 = Polygon(E_1, B_1, I_3)
t10, v_8, c_8, i_6 = Polygon(C_1, I_1, V_2)
t11, h_8, j_8, k_8 = Polygon(J_1, K_1, H_1)
t12, b_9, a_8, e_8 = Polygon(A_3, E_3, B_3)
t13, l_6, c_9, k_9 = Polygon(C_3, K_2, L_2)
t14, e_9, h_9, o_6 = Polygon(H_2, O_2, E_2)
t15, s_5, m_6, n_6 = Polygon(M_2, N_2, S_1)
t16, s_6, t_5, t_6 = Polygon(T_1, T_2, S_2)
t17, w_7, u_5, z_8 = Polygon(U_2, Z_2, W_2)
t18, g_8, r_6, u_6 = Polygon(R_1, U_1, G_3)
t19, j_9, v_9, w_8 = Polygon(V_1, W_1, J_2)
t20, a_9, z_9, g_9 = Polygon(Z_1, G_2, A_2)
w = 0 (slider from 0 to 2, step 0.1)
distanciaP1O1 = Distance(P_1, O_1)
TextoP1O1: Name[P_1] + (Name[O_1]) + " = " + distanciaP1O1
distanciaO1F3 = Distance(O_1, F_3)
TextoO1F3: Name[O_1] + (Name[F_3]) + " = " + distanciaO1F3
texto1: "Arista del dodecaedro " + L + ""
v10: (10 * v)
w5: (5 * w)
texto2: "Velocidad de giro " + v10 + ""
texto4: "Velocidad del corte " + w5 + ""