Schonhardt Polyhedron

C0 = 0.826445825140534740049120323293 = sqrt(1 + sqrt(3)) / 2
C1 = 0.866025403784438646763723170753 = sqrt(3) / 2

V0 = ( 0.0,  1.0,  C0)
V1 = (-1.0,  0.0, -C0)
V2 = (  C1, -0.5,  C0)
V3 = ( 0.5,   C1, -C0)
V4 = ( 0.5,  -C1, -C0)
V5 = ( -C1, -0.5,  C0)

Faces:
{ 0, 2, 4 }
{ 0, 4, 3 }
{ 0, 3, 5 }
{ 0, 5, 2 }
{ 1, 2, 5 }
{ 1, 5, 3 }
{ 1, 3, 4 }
{ 1, 4, 2 }