Icosaedro en el aire

Algunas diagonales espaciales del icosaedro están en proporción áurea con su arista.

Arista

Radio

Ver el icosaedro

RA = 1 (slider from 0 to 1, step 1)
p = 1.1755705045849463
t = 1.7320508075688772
c = 1.4142135623730951
n = 3 (slider from 3 to 5, step 1)
L = 5 (slider from 1 to 6, 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)
A' = Rotate(A, (360 * ° / n), O)
A'' = Rotate(A', (360 * ° / n), O)
v = 0.4 (slider from -2 to 2, step 0.2)
b = Distance(A, A')
arista = Distance(A, A')
radio = Distance(O, A'')
p20, B, C, D, E, F, G, H, I, J, caraAA'A'', caraAA''D, caraADE, caraABE, caraAA'B, caraA'BF, caraA'CF, caraA'A''C, caraA''CG, caraA''DG, caraCFI, caraCGI, caraGIJ, caraDGJ, caraFHI, caraHIJ, caraEHJ, caraDEJ, caraBFH, caraBEH, aristaAA'', aristaAA', aristaA'A'', aristaAD, aristaA''D, aristaAE, aristaDE, aristaAB, aristaBE, aristaA'B, aristaA'F, aristaBF, aristaA'C, aristaCF, aristaA''C, aristaA''G, aristaCG, aristaDG, aristaCI, aristaFI, aristaGI, aristaGJ, aristaIJ, aristaDJ, aristaHI, aristaFH, aristaHJ, aristaEJ, aristaEH, aristaBH = Icosahedron(A, A', A'')
f = Segment(J, F)
g = Segment(A', D)
c1, j, h, f_1, i = Polygon(J, H, F, I)
c2, d, a'', a', a = Polygon(D, A'', A', A)
k = Segment(C, B)
l = Segment(E, G)
K: G
c3, i_1, k_1, a''_1, c_1 = Polygon(I, K, A'', C)
c4, h_1, e, a_1, b_1 = Polygon(H, E, A, B)
m = Segment(I, A'')
q = Segment(A, H)
c6, j_1, e_2, d_1, k_3 = Polygon(J, E, D, K)
c5, a'_1, c_2, f_2, b_2 = Polygon(A', C, F, B)
o = false
texto1: "Arista del icosaedro " + L + ""
v5: (5 * v)
texto2: "Velocidad de giro " + v5 + ""