Plantilla 2

Esta plantilla permite construir poliedros regulares controlando valor de arista o radio del poliedro.
Si RA=0, el valor que muestra L es el radio. SI RA=1 el valor de L es la arista.

Borra el cubo representado y construye el poliedro que se desee.

Dodecaedro

Icosaedro

Poliedro dual

Intersección

Envolvente

Icosidodecaedro

Triacontaedro rómbico

Dodecaedro

Ver poliedros encajados

Oculta dodecaedro

Oculta icosaedro

Icosaedro

Dodecaedro

Icosaedro

Dodecaedro ↔ Icosaedro

Longitud arista

O: (0, 0, 0)
L = 2.4 (slider from 1 to 3, step 0.1)
p = 1.1755705045849463
ar: L / p
ci = Circle(O, ar, xOyPlane)
D1 = Point(ci)
D2 = Rotate(D1, 72°, zAxis)
D3 = Rotate(D2, 72°, zAxis)
a, D4, D5, D6, D7, D8, D9, D10, D11, D12, D13, D14, D15, D16, D17, D18, D19, D20, caraAA'A''BC, caraACGNH, caraAA'DIH, caraA'A''EJD, caraA''BFKE, caraBCGMF, caraGMSTN, caraHIPTN, caraDIPQJ, caraEJQRK, caraFKRSM, caraPQRST, aristaAC_1, aristaAA', aristaA'A'', aristaA''B, aristaBC_1, aristaAH, aristaCG_1, aristaGN, aristaHN, aristaHI_1, aristaDI_1, aristaA'D, aristaDJ_1, aristaEJ, aristaA''E, aristaEK_1, aristaFK, aristaBF_1, aristaFM_1, aristaGM_1, aristaMS, aristaST_1, aristaNT_1, aristaPT, aristaIP, aristaPQ, aristaJQ, aristaQR_1, aristaKR, aristaRS = Dodecahedron(D1, D2, D3)
O' = Midpoint(D3, D20)
t = 1 (slider from 1 to hom, step 0.001)
hom: (5 - sqrt(5)) / 2
t_1 = 1.7320508075688772
c = 1.4142135623730951
caso = 1 (slider from 1 to 3, step 1)
i1: false
i3: false
i4: false
j: true
f = OrthogonalLine(O', caraHIPTN)
g = OrthogonalLine(O', caraPQRST)
h = OrthogonalLine(O', caraGMSTN)
A = Intersect(f, caraHIPTN)
B = Intersect(g, caraPQRST)
C = Intersect(h, caraGMSTN)
A' = Dilate(A, t, O')
B' = Dilate(B, t, O')
C' = Dilate(C, t, O')
b, D, E, F, G, H, I, J, K, M, caraA'B'C', caraA'C'F, caraC'FG, caraC'DG, caraB'C'D, caraB'DH, caraB'EH, caraA'B'E, caraA'EI, caraA'FI, caraEHK, caraEIK, caraIKM, caraFIM, caraHJK, caraJKM, caraGJM, caraFGM, caraDHJ, caraDGJ, aristaA'C', aristaB'C', aristaA'B', aristaC'F, aristaA'F, aristaC'G, aristaFG, aristaC'D, aristaDG, aristaB'D, aristaB'H, aristaDH, aristaB'E, aristaEH, aristaA'E, aristaA'I, aristaEI, aristaFI, aristaEK, aristaHK, aristaIK, aristaIM, aristaKM, aristaFM, aristaJK, aristaHJ, aristaJM, aristaGM, aristaGJ, aristaDJ = Icosahedron(C', B', A')
i = OrthogonalLine(O', caraB'EH)
N = Intersect(i, caraB'EH)
k = OrthogonalLine(O', caraA'B'E)
l = OrthogonalLine(O', caraA'B'C')
P = Intersect(l, aristaB'C')
Q = Intersect(l, caraA'B'C')
R = Intersect(k, caraA'B'E)
d, S, T, U, V, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, caraNRQST, cara2, cara1, cara3, cara4, cara5, cara9, cara10, cara6, cara7, cara8, cara11, aristaNT, aristaNR, aristaQR, aristaQS, aristaST, arista1, aristaTZ, arista9, arista11, arista10, arista2, aristaRU, arista3, arista4, aristaQV, arista5, arista6, aristaSW, arista7, arista8, arista15, arista21, arista16, arista18, arista12, arista17, arista13, arista19, arista14, arista20 = Dodecahedron(N, R, Q)
hom2: (9 - (3 * sqrt(5))) / 2
L_1 = Midpoint(aristaQR_1)
M_1 = Midpoint(aristaRS)
N_1 = Midpoint(aristaPT)
O_1 = Midpoint(aristaPQ)
P_1 = Midpoint(aristaST_1)
Q_1 = Midpoint(aristaMS)
R_1 = Midpoint(aristaKR)
S_1 = Midpoint(aristaJQ)
T_1 = Midpoint(aristaIP)
U_1 = Midpoint(aristaNT_1)
V_1 = Midpoint(aristaFM_1)
W_1 = Midpoint(aristaGM_1)
Z_1 = Midpoint(aristaFK)
A_2 = Midpoint(aristaEK_1)
B_2 = Midpoint(aristaEJ)
C_2 = Midpoint(aristaA''E)
D_2 = Midpoint(aristaA''B)
E_2 = Midpoint(aristaBF_1)
F_2 = Midpoint(aristaCG_1)
G_2 = Midpoint(aristaGN)
H_2 = Midpoint(aristaHN)
I_2 = Midpoint(aristaHI_1)
J_2 = Midpoint(aristaAH)
K_2 = Midpoint(aristaDI_1)
L_2 = Midpoint(aristaDJ_1)
M_2 = Midpoint(aristaA'D)
N_2 = Midpoint(aristaAA')
O_2 = Midpoint(aristaA'A'')
P_2 = Midpoint(aristaBC_1)
Q_2 = Midpoint(aristaAC_1)
penta1, n_1, o_1, l_1, m_1, p_1 = Polygon(N_1, O_1, L_1, M_1, P_1)
penta2, o_2, s_1, l_2, k_2, t_2 = Polygon(O_1, S_1, L_2, K_2, T_1)
penta3, u_1, n_2, t_3, i_2, h_2 = Polygon(U_1, N_1, T_1, I_2, H_2)
penta4, q_1, p_2, u_2, g_2, w_1 = Polygon(Q_1, P_1, U_1, G_2, W_1)
penta5, r_1, m_2, q_2, v_1, z_1 = Polygon(R_1, M_1, Q_1, V_1, Z_1)
penta6, s_2, l_3, r_2, a_2, b_2 = Polygon(S_1, L_1, R_1, A_2, B_2)
lista1: {penta1, penta2, penta3, penta4, penta5, penta6}
lista1' = Mirror(lista1, O')
lista2 = Translate({lista1, lista1'}, Vector[A, A])
tri1, r_3, l_4, m_3 = Polygon(L_1, M_1, R_1)
tri2, a_1, r_4, z_2 = Polygon(R_1, Z_1, A_2)
tri3, e_2, z_3, v_2 = Polygon(Z_1, V_1, E_2)
tri4, p_3, d_2, e_1 = Polygon(D_2, E_2, P_2)
lista3 = Sequence(Rotate[{tri1, tri2, tri3, tri4}, ((i * 72))°, zAxis], i, 0, 4)
rom1, b', d19, d_1, d18 = Polygon(B', D19, D, D18)
rom2, d_3, d19_1, c', d14 = Polygon(D, D19, C', D14)
rom3, d14_1, c'_1, d9, g_1 = Polygon(D14, C', D9, G)
rom4, d_4, d14_2, g_3, d8 = Polygon(D, D14, G, D8)
rom5, g_4, d9_1, f_1, d5 = Polygon(G, D9, F, D5)
rom6, d4, g_5, d5_1, m = Polygon(D4, G, D5, M)
lista4: {rom1, rom2, rom3, rom4, rom5, rom6}
lista5 = Sequence(Rotate[lista4, ((i * 72))°, zAxis], i, 0, 4)
e: false
e1: false
n = Distance(D3, D4)