Dodecaedro rómbico

Construimos las seis pirámides que unen cada una de las caras del cubo con su centro.
 Si hacemos la simetría de cada una de esas pirámides respecto de la cara del cubo correspondiente, se obtiene un poliedro con 12 caras rómbicas que rellena el espacio.

Arista

Radio

Empaquetamiento

SI

SI

NO

NO

Ver empaquetamiento

Animación

Cubo

Pirámides interiores

Dodecaedro rómbico

Empaquetamiento

Detener la animación en:

t = 0.999 (slider from -1 to 6, step 0.001)
t3 = Min(1, Max[0, t - 2])
t1 = Min(1, t)
O: (0, 0, 0)
L = 3 (slider from 1 to 4, step 0.1)
n = 4 (slider from 3 to 5, step 1)
c = 1.4142135623730951
t_1 = 1.7320508075688772
p = 1.1755705045849463
ar = If(n ≟ 3, L / t_1, 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)
p06, B, C, D, E, F, caraAA'A''B, caraABFC_1, caraAA'DC, caraA'A''ED, caraA''BFE, caraCDEF, aristaAB_1, aristaAA', aristaA'A'', aristaA''B, aristaAC_1, aristaBF_1, aristaCF_1, aristaCD, aristaA'D, aristaDE, aristaA''E, aristaEF = Cube(A, A', A'')
w = Vector(B, E)
G = Midpoint(A, E)
f = OrthogonalLine(G, caraABFC_1)
H = Intersect(f, caraABFC_1)
P: H - (t1 * (G - H))
a0, caraABFC, caraABP, caraACP, caraCFP, caraBFP, aristaAB, aristaAC, aristaCF, aristaBF, aristaBP, aristaAP, aristaCP, aristaFP = Pyramid(B, A, C, F, P)
u = Vector(B, C)
t2 = Min(1, Max[0, t - 1])
v = 0.4 (slider from -2 to 2, step 0.2)
arista = Distance(A, A')
radio = Distance(O, A'')
a1 = Mirror(a0, G)
g = Line(O, G)
a2 = Rotate(a0, 90°, g)
a3 = Rotate(a0, -90°, g)
a4 = Rotate(a2, 90°, f)
b0 = Translate(a0, Vector[(t2 * u)])
a5 = Rotate(a2, -90°, f)
b1 = Translate(a1, Vector[(t2 * u)])
b2 = Translate(a2, Vector[(t2 * u)])
b3 = Translate(a3, Vector[(t2 * u)])
b4 = Translate(a4, Vector[(t2 * u)])
c0 = Translate(a0, Vector[(t3 * w)])
b5 = Translate(a5, Vector[(t2 * u)])
c1 = Translate(a1, Vector[(t3 * w)])
c2 = Translate(a2, Vector[(t3 * w)])
c3 = Translate(a3, Vector[(t3 * w)])
c4 = Translate(a4, Vector[(t3 * w)])
c5 = Translate(a5, Vector[(t3 * w)])
i = 0 (slider from 0 to 1, step 1)
e = true
j = 1 (slider from 0 to 1, step 1)
nada = -2.8 (slider from -5 to 5, step 0.1)
texto2: "Arista del cubo  " + L + ""
v5: (5 * v)
texto3: "Velocidad de giro " + v5 + ""