Pentagonal Trapezohedron-Antiprism Toroid

C0 = 0.236067977499789696409173668731 = sqrt(5) - 2
C1 = 0.618033988749894848204586834366 = (sqrt(5) - 1) / 2
C2 = 1.23606797749978969640917366873  = sqrt(5) - 1
C3 = 1.38196601125010515179541316563  = (5 - sqrt(5)) / 2
C4 = 1.61803398874989484820458683437  = (1 + sqrt(5)) / 2
C5 = 2.23606797749978969640917366873  = sqrt(5)
C6 = 2.61803398874989484820458683437  = (3 + sqrt(5)) / 2

V0  = (  C1,  -C2,  C5)
V1  = (  C1,  -C2, -C5)
V2  = ( -C1,   C2,  C5)
V3  = ( -C1,   C2, -C5)
V4  = (-2.0, -1.0,  C3)
V5  = (-2.0, -1.0, -C3)
V6  = ( 2.0,  1.0,  C3)
V7  = ( 2.0,  1.0, -C3)
V8  = ( -C0,  -C6, 0.0)
V9  = (  C0,   C6, 0.0)
V10 = ( 0.0, -1.0,  C6)
V11 = ( 0.0, -1.0, -C6)
V12 = ( 0.0,  1.0,  C6)
V13 = ( 0.0,  1.0, -C6)
V14 = ( -C4,  -C4,  C4)
V15 = ( -C4,  -C4, -C4)
V16 = (  C4,   C4,  C4)
V17 = (  C4,   C4, -C4)
V18 = (-1.0,  -C6, 0.0)
V19 = ( 1.0,   C6, 0.0)

Faces:
{  0,  6, 16, 12, 10 }
{  1,  8, 18, 15, 11 }
{  2,  4, 14, 10, 12 }
{  3,  9, 19, 17, 13 }
{  4,  5, 15, 18, 14 }
{  5,  3, 13, 11, 15 }
{  6,  7, 17, 19, 16 }
{  7,  1, 11, 13, 17 }
{  8,  0, 10, 14, 18 }
{  9,  2, 12, 16, 19 }
{  2,  6,  0 }
{  2,  0,  4 }
{  3,  1,  7 }
{  3,  7,  9 }
{  4,  0,  8 }
{  4,  8,  5 }
{  5,  8,  1 }
{  5,  1,  3 }
{  6,  2,  9 }
{  6,  9,  7 }