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.

Arista

Radio

Ejes centros caras

Ejes por vértices

Planos de simetría

6

10

15

Elementos de simetría

Ejes por aristas

15

β = 3.141592653589793 rad (slider from 0 to 180°, step 0.001°)
e = 4.6 (slider from -5 to 5, step 0.1)
O: (0, 0, 0)
L = 2.5 (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)
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'')
N_2 = Midpoint(aristaA'A'')
M_2 = Midpoint(aristaST)
r = Line(M_2, N_2)
U = Midpoint(A'', T)
k = OrthogonalLine(U, caraA'A''EJD)
g = OrthogonalLine(U, caraPQRST)
V = Intersect(k, g)
d = Sphere(V, e)
O_2, P_2 = Intersect(r, d)
e2 = Segment(O_2, P_2)
v = 0 (slider from -1 to 1, step 0.1)
b = Distance(A, A')
arista = Distance(A, A')
radio = Distance(O, A'')
a = 4.1 (slider from 0 to 6, step 0.1)
o1 = true
o2 = false
w = 1 (slider from -5 to 5, step 0.1)
v10: (10 * v)
o3 = false
f = OrthogonalLine(U, caraFKRSM)
h = OrthogonalLine(U, caraEJQRK)
i = OrthogonalLine(U, caraEJQRK)
j = OrthogonalLine(U, caraDIPQJ)
l = OrthogonalLine(U, caraHIPTN)
W, Z = Intersect(l, d)
A_1 = Intersect(aristaHN, d)
B_1, C_1 = Intersect(j, d)
D_1, E_1 = Intersect(g, d)
F_1, G_1 = Intersect(i, d)
H_1, I_1 = Intersect(f, d)
J_1, K_1 = Intersect(k, d)
m = Segment(F_1, G_1)
q = Segment(I_1, H_1)
e1 = Segment(E_1, D_1)
f_1 = Segment(C_1, B_1)
g_1 = Segment(J_1, K_1)
h_1 = Line(Q, C)
i_1 = Line(R, A)
j_1 = Line(S, A')
L_1 = Intersect(aristaPQ, aristaIP)
k_1 = Line(L_1, B)
l_1 = Line(T, A'')
m_1 = Line(J, G)
n_1 = Line(H, K)
p_1 = Line(E, N)
M_1 = Intersect(m_1, aristaGN)
r_1 = Line(I, F)
N_1, O_1 = Intersect(i_1, d)
P_1, Q_1 = Intersect(n_1, d)
R_1, S_1 = Intersect(m_1, d)
T_1, U_1 = Intersect(k_1, d)
V_1, W_1 = Intersect(l_1, d)
Z_1, A_2 = Intersect(j_1, d)
B_2, C_2 = Intersect(p_1, d)
F_2, G_2 = Intersect(h_1, d)
H_2 = Intersect(f_1, r_1)
I_2, J_2 = Intersect(f_1, d)
K_2, L_2 = Intersect(r_1, d)
e3 = Segment(A_2, Z_1)
t_1 = Segment(V_1, W_1)
a_1 = Segment(U_1, T_1)
b_1 = Segment(L_2, K_2)
c_1 = Segment(P_1, Q_1)
d_1 = Segment(O_1, N_1)
f_2 = Segment(G_2, F_2)
g_2 = Segment(C_2, B_2)
h_2 = Segment(S_1, R_1)
q_1 = Line(D, M)
D_2, E_2 = Intersect(q_1, d)
i_2 = Segment(D_2, E_2)
o = Plane(R, P_1, A)
p122 = Rotate(p12, β, e2)
texto1: "Arista del dodecaedro " + L + ""
o4 = true
α = 1.2566370614359172 rad (slider from 0 to 72°, step 0.1°)
γ = 2.0943951023931953 rad (slider from 0 to 120°, step 0.001°)
p121 = Rotate(p12, α, e1)
p123 = Rotate(p12, γ, e3)
v11: floor(v10)
texto2: "Veloc. rotación " + v10 + "" + v11 + ""