Cinco tetraedros en un dodecaedro

Primero los vemos de uno en uno. después se van agregando para verlos todos juntos. Las aristas de los tetraedros van sobre las diagonales de los cubos de la aplicación anterior.

Cinco tetraedros

Animación

Detener la animación en:

t1 = 15 (slider from 0 to 15, step 0.001)
O: (0, 0, 0)
L = 3 (slider from 1 to 4, step 0.1)
n = 5 (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 = 0.4 (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)
F_1 = Intersect(aristaCG, aristaJQ)
I_2 = Intersect(aristaBF, aristaBC)
w = 0 (slider from 0 to 2, step 0.1)
texto1: "Arista del dodecaedro " + L + ""
v10: (10 * v)
w5: (5 * w)
texto2: "Velocidad de giro " + v10 + ""
texto4: "Veloc. animación " + w5 + ""
p041, N_1, cara19, cara20, cara21, cara22, arista33, arista34, arista35, arista36, arista37, arista38 = Tetrahedron(Q, N, F)
p042, A_2, caraGIR, cara36, cara37, cara35, aristaGR, aristaIR, aristaGI, arista62, arista60, arista61 = Tetrahedron(R, I, G)
p043, C_2, cara38, cara39, cara40, cara41, arista63, arista64, arista65, arista66, arista67, arista68 = Tetrahedron(P, A, M)
p045, D_2, cara42, cara43, cara44, cara48, arista69, arista70, arista71, arista75, arista76, arista77 = Tetrahedron(S, B, J)
p044, V, caraCKT, caraKTV, caraCTV, caraCKV, aristaKT, aristaCT, aristaCK, aristaTV, aristaKV, aristaCV = Tetrahedron(T, C, K)
p041b: p041
p042b: p042
p043b: p043
p044b: p044
p045b: p045