Elongated Triangular Dipyramid

C0 = 0.288675134594812882254574390251 = sqrt(3) / 6
C1 = 0.577350269189625764509148780502 = sqrt(3) / 3
C2 = 1.31649658092772603273242802490  = (3 + 2 * sqrt(6)) / 6

V0 = ( 0.5, -C0,  0.5)
V1 = ( 0.5, -C0, -0.5)
V2 = (-0.5, -C0,  0.5)
V3 = (-0.5, -C0, -0.5)
V4 = ( 0.0,  C1,  0.5)
V5 = ( 0.0,  C1, -0.5)
V6 = ( 0.0, 0.0,   C2)
V7 = ( 0.0, 0.0,  -C2)

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