Tetraedrp

El tetraedro tiene cuatro ejes de simetría que unen cada arista con el centro de la cara opuesta.
Los cuatro planos de simetría pasan por cada par de vértices contiguos y el punto medio de la arista opuesta.

Arista

Radio

Ejes de rotación

Ejes centros aristas

Planos de simetría

4

6

6

Elementos de simetría

Ejes  vértices-caras

3

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 = 6 (slider from 1 to 8, 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 = 5.2 (slider from -5 to 6, step 0.1)
texto2: "Veloc. rotación " + v10 + ""
o2 = false
α = 2.0943951023931953 rad (slider from 0 to 120°, step 0.01°)
β = 3.141592653589793 rad (slider from 0 to 180°, step 0.01°)
γ = 1.2564625285107178 rad (slider from 0 to 72°, step 0.01°)
A2 = Rotate(A1, 120°, O)
A3 = Rotate(A2, 120°, O)
o = 1.4 (slider from 1 to 2, step 0.01)
texto1: "Arista del tetraedro " + L + ""
p04, B, caraAA1A2, caraAA2B, caraAA1B, caraA1A2B, aristaAA2, aristaAA1, aristaA1A2, aristaAB, aristaA2B, aristaA1B = Tetrahedron(A, A1, A2)
f = Line(B, O)
C = Midpoint(aristaAA1)
D = Midpoint(aristaAB)
g = Segment(A1, D)
h = Segment(B, C)
E = Intersect(h, g)
i = Line(E, A2)
F = Intersect(f, i)
j = Line(A, F)
k = Line(A1, F)
d = Sphere(F, e)
G, H = Intersect(i, d)
I, J = Intersect(j, d)
K, M = Intersect(k, d)
N, P = Intersect(f, d)
l = Segment(P, N)
m = Segment(M, K)
r = Segment(I, J)
q = Segment(G, H)
p041 = Rotate(p04, α, l)
s = Plane(B, C, A2)
Q = Midpoint(A1, A2)
R = Midpoint(B, A1)
S = Midpoint(A2, A)
T = Midpoint(A2, B)
f_1 = Line(R, S)
g_1 = Line(Q, D)
h_1 = Line(C, T)
U, V = Intersect(h_1, d)
W, Z = Intersect(f_1, d)
i_1 = Segment(W, Z)
j_1 = Segment(V, U)
A_1 = Point(g_1)
B_1 = Point(g_1)
k_1 = Segment(A_1, B_1)
p042 = Rotate(p04, β, k_1)