Posición inicial

Tensar

Icosaedro de Jessen

Barra:cable = $\frac{2·\sqrt{6}}{3}$≈1.63299

Partimos de barras pegadas 
dos a dos. Al tensar, las barras 
se separan hasta que la dirección 
de la fuerza resultante coincida 
con la barra. 

Resultará una estructura 
formada por tres pares 
de barras paralelas, 
perpendiculares entre sí, 
conocida como 
icosaedro de Jessen.

barra = 10 (slider from 4 to 16, step 1)
s: barra / 2
c1, f, g, h, l = Polygon((0.001, 0.001, (-s)), (s, 0.001, (-s)), (s, s, (-s)), (0.001, s, (-s)))
A1 = PointIn(c1)
b: y(A1)
a: x(A1)
t: abs((a, b, 0))
A9: (((-s) * b / t), (s * a / t), t)
A10: (x(A9), y(A9), (-z(A9)))
A6: ((s * a / t) + b, (s * b / t) - a, 0)
A3: (a, b, s)
A2: ((-a), (-b), (-s))
A5: ((s * a / t) - b, (s * b / t) + a, 0)
A7: (-A6)
A4: ((-a), (-b), s)
A11: (-A10)
A8: (-A5)
A12: (-A9)
barrasAzules: {Segment[A1, A3], Segment[A2, A4]}
barrasRojas: {Segment[A5, A7], Segment[A6, A8]}
barrasVerdes: {Segment[A9, A11], Segment[A10, A12]}
aristas: {Segment[A1, A5], Segment[A1, A6], Segment[A1, A10], Segment[A1, A12], Segment[A2, A7], Segment[A2, A8], Segment[A2, A10], Segment[A2, A12], Segment[A3, A5], Segment[A3, A6], Segment[A3, A9], Segment[A3, A11], Segment[A4, A7], Segment[A4, A8], Segment[A4, A9], Segment[A4, A11], Segment[A5, A9], Segment[A5, A10], Segment[A6, A11], Segment[A6, A12], Segment[A7, A9], Segment[A7, A10], Segment[A8, A11], Segment[A8, A12]}
anima = 100 (slider from 0 to 100, step 0.1)
n = 50 (slider from 1 to 1000000, step 1)
proporción: (2 * s / Element[aristas, 1])
u: ((2.2 * s) * UnitVector[Vector[A1, A5] + Vector[A1, A6] + Vector[A1, A10] + Vector[A1, A12]])
velocidad = 1 (slider from 1 to 10, step 1)
A: (A9 + A11) / 2
α = Angle(A3, A, A4)
j: (s * sqrt(2) / 4)
B1: (j, j, (-s))
B2: ((-j), (-j), (-s))
B3: (j, j, s)
B4: ((-j), (-j), s)
B5: (j, (3 * j), 0)
B6: ((3 * j), j, 0)
B7: ((-3 * j), (-j), 0)
B8: ((-j), (-3 * j), 0)
B9: ((-2 * j), (2 * j), s / 2)
B10: ((-2 * j), (2 * j), ((-s)) / 2)
B11: ((2 * j), (-2 * j), s / 2)
B12: ((2 * j), (-2 * j), ((-s)) / 2)
jessen1: {Polygon[B1, B5, B10], Polygon[B1, B6, B12], Polygon[B2, B7, B10], Polygon[B2, B8, B12], Polygon[B3, B5, B9], Polygon[B3, B6, B11], Polygon[B4, B7, B9], Polygon[B4, B8, B11]}
jessen2: {Polygon[B1, B3, B5], Polygon[B1, B3, B6], Polygon[B1, B10, B12], Polygon[B2, B10, B12], Polygon[B2, B4, B7], Polygon[B2, B4, B8], Polygon[B3, B9, B11], Polygon[B4, B9, B11], Polygon[B5, B7, B9], Polygon[B5, B7, B10], Polygon[B6, B8, B11], Polygon[B6, B8, B12]}
verJessen = false
diedro: {Polygon[A3, A9, A11], Polygon[A4, A9, A11]}
texto2: "Barra:cable = " + proporción + ""
texto4: "α = " + α + ""