Hexagonal Dipyramid

C0 = 0.577350269189625764509148780502 = sqrt(3) / 3
C1 = 1.15470053837925152901829756100  = 2 * sqrt(3) / 3

V0 = ( 0.0, 0.0,  2.0)
V1 = ( 0.0, 0.0, -2.0)
V2 = ( 1.0,  C0,  0.0)
V3 = ( 1.0, -C0,  0.0)
V4 = (-1.0,  C0,  0.0)
V5 = (-1.0, -C0,  0.0)
V6 = ( 0.0,  C1,  0.0)
V7 = ( 0.0, -C1,  0.0)

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