Hexagonal Antiprism

C0 = 0.427799838583676096484617883106 = sqrt(sqrt(3) - 1) / 2
C1 = 0.866025403784438646763723170753 = sqrt(3) / 2

V0  = ( 1.0,  0.0,  C0)
V1  = (-1.0,  0.0,  C0)
V2  = ( 0.5,   C1,  C0)
V3  = ( 0.5,  -C1,  C0)
V4  = (-0.5,   C1,  C0)
V5  = (-0.5,  -C1,  C0)
V6  = (  C1,  0.5, -C0)
V7  = (  C1, -0.5, -C0)
V8  = ( -C1,  0.5, -C0)
V9  = ( -C1, -0.5, -C0)
V10 = ( 0.0,  1.0, -C0)
V11 = ( 0.0, -1.0, -C0)

Faces:
{  0,  2,  4,  1,  5,  3 }
{  6,  7, 11,  9,  8, 10 }
{  0,  3,  7 }
{  0,  7,  6 }
{  1,  4,  8 }
{  1,  8,  9 }
{  2,  0,  6 }
{  2,  6, 10 }
{  3,  5, 11 }
{  3, 11,  7 }
{  4,  2, 10 }
{  4, 10,  8 }
{  5,  1,  9 }
{  5,  9, 11 }