 \sqrt{ 2 } 

 \sqrt{ 3 } 

1

 \sqrt{ \frac{2}{3} } 

\frac{1}{ \sqrt{ 3 } }

voir

voir1

Cube

In what sense seems to turn this cube?

(change eye or speed of the rotation)

R = 0.9 (slider from 0 to 5, step 0.1)
O = (-1.2414860080132766, -0.8918474741272644)
zoom = 3 (slider from 1 to 5, step 1)
View3D = (-6.299584340918686, -0.16926199799792013)
C = (-8.806869297750172, -1.2518541532913536)
Z: C + (-zoom * sin(x(View3D)) * sin(y(View3D)), zoom * cos(y(View3D)))
w = Vector(C, Z)
Y: C + (zoom * cos(x(View3D)), zoom * 0)
v = Vector(C, Y)
X: C + (-zoom * sin(x(View3D)) * cos(y(View3D)), -zoom * sin(y(View3D)))
u = Vector(C, X)
C_3: R * sqrt(2 / 3) * v + R * sqrt(1 / 3) * w + O
C_1: -R * sqrt(1 / 2) * u - R * sqrt(1 / 6) * v + R * sqrt(1 / 3) * w + O
C_2: R * sqrt(1 / 2) * u - R * sqrt(1 / 6) * v + R * sqrt(1 / 3) * w + O
a = Segment(C_1, O)
c = Segment(O, C_2)
B_1: -1 * R * 1 / sqrt(2) * u + R * sqrt(1 / 6) * v + 2 * R * sqrt(3) / 3 * w + O
B_2: -1 * R * sqrt(2 / 3) * v + 2 * R * sqrt(3) / 3 * w + O
B_3: R / sqrt(2) * u + R / sqrt(6) * v + 2 * R * sqrt(3) / 3 * w + O
d = Segment(B_3, C_3)
e = Segment(B_3, C_2)
f = Segment(C_3, B_1)
g = Segment(B_1, C_1)
h = Segment(C_1, B_2)
j = Segment(B_2, C_2)
B: R * sqrt(3) * w + O
k = Segment(B, B_2)
l = Segment(B, B_1)
m = Segment(B, B_3)
C': R * sqrt(2 / 3) * v + O
n = Segment(C_3, C')
Q: 1 / sqrt(3) * w + O
s = Segment(Q, C_3)
poly1, o, b, c_1 = Polygon(B, C_3, O)
T_1: u + v + 0 * w + O
T_2: -1 * u + v + 0 * w + O
T_3: -1 * u - v + 0 * w + O
T_4: u - v + 0 * w + O
poly2, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
M_1 = Midpoint(B, C_3)
M_2 = Midpoint(C_3, O)
M_3 = Midpoint(Q, C_3)
q = false
r = false
t_5 = Segment(C_3, O)
i = Line(B, O)
p = Ray(O, B)
a_1 = Segment(O, B)
t = 0.95 (slider from 0 to 6.283185307179586, step 0.01)
A = Midpoint(a_1)
E: R * sqrt(2 / 3) * cos(t + π / 2) * u + R * sqrt(2 / 3) * sin(t + π / 2) * v + R * sqrt(1 / 3) * w + O
F: R * sqrt(2 / 3) * cos(t + π / 2 + 120°) * u + R * sqrt(2 / 3) * sin(t + π / 2 + 120°) * v + R * sqrt(1 / 3) * w + O
G: R * sqrt(2 / 3) * cos(t + π / 2 + 240°) * u + R * sqrt(2 / 3) * sin(t + π / 2 + 240°) * v + R * sqrt(1 / 3) * w + O
H: R * sqrt(2 / 3) * cos(-t - 30°) * u - R * sqrt(2 / 3) * sin(-t - 30°) * v + 2 * R * sqrt(3) / 3 * w + O
b_1 = Segment(H, E)
d_1 = Segment(E, O)
e_1 = Segment(H, G)
f_1 = Segment(G, O)
D: R * sqrt(2 / 3) * cos(-t + 90°) * u - R * sqrt(2 / 3) * sin(-t + 90°) * v + 2 * R * sqrt(3) / 3 * w + O
I = Intersect(d_1, f_1)
poly1_1, d_2, g_1, i_1, f_2 = Polygon(D, G, I, F)
J: R * sqrt(2 / 3) * cos(-t - 150°) * u - R * sqrt(2 / 3) * sin(-t - 150°) * v + 2 * R * sqrt(3) / 3 * w + O
poly3, j_1, e_2, i_2, f_3 = Polygon(J, E, I, F)
poly4, j_2, b_2, h_1, e_3 = Polygon(J, B, H, E)
K = Intersect(b_2, j_2)
poly5, k_1, d_3, f_4, j_3 = Polygon(K, D, F, J)
poly6, k_2, d_4, g_2, h_2 = Polygon(K, D, G, H)
L = Intersect(b_2, j_2)
l_1 = Segment(L, I)
Speed = 6.3 (slider from 0 to 10, step 0.1)
z = false
poly7, o_1, b_3, e_4 = Polygon(B, E, O)
m_1 = Segment(E, O)
M = Midpoint(b_3)
N = Midpoint(E, B)