Cubo y Octaedro

El cubo y el octaedro comparten los ejes de rotación. Los que unen vértices opuestos en el cubo son los que pasan por los centros de caras opuestas en el octaedro y viceversa.
Los planos de simetría son 9. Hay dos tipos distintos, de uno de ellos hay 6 planos y 3 del otro tipo.

Arista

Radio

Ejes tipo 1

Ejes centros aristas

Planos de simetría

6

Elementos de simetría

Ejes  tipo 3

6

Cubo

Cubo

Octaedro

Octaedro

Poliedro

3

y

RA = 1 (slider from 0 to 1, step 1)
p = 1.1755705045849463
t = 1.7320508075688772
c = 1.4142135623730951
n = 4 (slider from 3 to 5, step 1)
L = 4 (slider from 1 to 5, step 0.1)
ar = If(n ≟ 3, L / t, If[n ≟ 4, L / c, If[n ≟ 5, L / p]])
des = If(RA ≟ 0, L, If[RA ≟ 1, ar])
O: (0, 0, 0)
ci = Circle(O, des, xOyPlane)
A = Point(ci)
A1 = Rotate(A, (360 * ° / n), O)
A' = Rotate(A1, (360 * ° / n), O)
v = 0 (slider from -1 to 1, step 0.001)
b = Distance(A, A1)
arista = Distance(A, A1)
radio = Distance(O, A')
a = 4.1 (slider from 0 to 6, step 0.1)
o1 = true
o4 = false
w = 1 (slider from -5 to 5, step 0.1)
v10: (10 * v)
o3 = false
e = 5.4 (slider from -5 to 6, step 0.1)
o2 = false
α = 0 rad (slider from 0 to 90°, step 0.01°)
β = 0 rad (slider from 0 to 180°, step 0.01°)
γ = 0 rad (slider from 0 to 120°, step 0.01°)
p06, K_2, L_2, M_2, N_2, O_2, cara1, cara3, cara2, cara4, cara5, cara6, arista1, aristaAA', aristaA'A'', arista4, arista2, arista6, arista8, arista7, arista3, arista9, arista5, arista10 = Cube(A, A1, A')
A2 = Rotate(A1, 120°, O)
A3 = Rotate(A2, 120°, O)
p0888, B, C, D, caraAA2A3, caraAA3D, caraABD, caraAA2B, caraA2BC, caraA2A3C, caraA3CD, caraBCD, aristaAA3, aristaAA2, aristaA2A3, aristaAD, aristaA3D, aristaAB, aristaBD, aristaA2B, aristaA2C, aristaBC, aristaA3C, aristaCD = Octahedron(A1, A2, A3)
E = Midpoint(C, M_2)
f = Line(E, O)
g = Line(C, A1)
F = Midpoint(arista10)
G = Midpoint(aristaAA')
h = Line(F, G)
J = Midpoint(C, A1)
d = Sphere(J, e)
K, M = Intersect(g, d)
N, P = Intersect(h, d)
Q, R = Intersect(f, d)
T = Midpoint(aristaA2A3)
H = Intersect(aristaBC, aristaBD)
i = Line(H, A3)
l = Segment(K, M)
q = Segment(Q, R)
k = Segment(N, P)
o = 1.4 (slider from 1 to 2, step 0.01)
I = Midpoint(aristaBC)
S = Midpoint(aristaAA3)
j = Line(S, I)
U, V = Intersect(j, d)
m = Segment(U, V)
p061 = Rotate(p06, α, q)
p062 = Rotate(p06, β, k)
p063 = Rotate(p06, γ, l)
r = Plane(A', N_2, L_2)
W = Midpoint(N_2, A')
Z = Midpoint(C, K_2)
A_1 = Midpoint(L_2, A)
s = Plane(W, Z, A_1)
B_1 = Midpoint(C, A)
C_1 = Midpoint(C, A')
D_1 = Midpoint(A1, N_2)
E_1 = Midpoint(M_2, A)
f_1 = Line(B_1, D_1)
g_1 = Line(E_1, C_1)
u = Sphere(J, C)
F_1 = Midpoint(q)
G_1, H_1 = Intersect(arista8, u)
B1, B5 = Intersect(q, u)
B3, B6 = Intersect(g_1, u)
B2, B4 = Intersect(f_1, u)
B1_1 = NaN
p08, I_1, J_1, K_1, cara7, cara8, cara9, cara10, cara11, cara12, cara13, cara14, arista11, arista12, arista13, arista14, arista15, arista16, arista17, arista18, arista19, arista20, arista21, arista22 = Octahedron(B1, B3, B2)
oo = 1 (slider from 0 to 1, step 1)
p081 = Rotate(p08, α, q)
δ: °
ε: °
p1 = 2.0943951023931953 rad
p3 = 1.5707963267948966 rad
s1 = 3
s3 = 4
P1 = NaN
p082 = Rotate(p08, β, k)
p083 = Rotate(p08, γ, l)
texto3: "" + s1 + ""
texto4: "" + s3 + ""
texto1: "Arista del cubo " + L + ""
v11: floor(v10)
texto2: "Veloc. rotación " + v11 + ""