Simplest Canonical Polyhedron with D3v Symmetry (1 of 2)

C0 = 0.585786437626904951198311275790 = 2 - sqrt(2)
C1 = 1.41421356237309504880168872421  = sqrt(2)

V0 = (0.0, 0.0,  C1)
V1 = (0.0, 0.0, -C1)
V2 = ( C1, 0.0, 0.0)
V3 = (-C1, 0.0, 0.0)
V4 = (0.0,  C1, 0.0)
V5 = (0.0, -C1, 0.0)
V6 = ( C0,  C0,  C0)
V7 = (-C0, -C0, -C0)

Faces:
{ 0, 4, 3 }
{ 0, 3, 5 }
{ 0, 5, 2 }
{ 1, 3, 4 }
{ 1, 4, 2 }
{ 1, 2, 5 }
{ 6, 0, 2 }
{ 6, 2, 4 }
{ 6, 4, 0 }
{ 7, 3, 1 }
{ 7, 1, 5 }
{ 7, 5, 3 }
