Pentagonal Antiprism-Trapezohedron Toroid

C0 = 0.190983005625052575897706582817 = (3 - sqrt(5)) / 4
C1 = 0.309016994374947424102293417183 = (sqrt(5) - 1) / 4
C2 = 0.809016994374947424102293417183 = (1 + sqrt(5)) / 4

V0  = ( 0.5,  0.0,   C2)
V1  = ( 0.5,  0.0,  -C2)
V2  = (-0.5,  0.0,   C2)
V3  = (-0.5,  0.0,  -C2)
V4  = ( 0.0,   C2,  0.5)
V5  = ( 0.0,   C2, -0.5)
V6  = ( 0.0,  -C2,  0.5)
V7  = ( 0.0,  -C2, -0.5)
V8  = (  C2,  0.5,  0.0)
V9  = ( -C2, -0.5,  0.0)
V10 = ( 0.0,   C0,  0.5)
V11 = ( 0.0,   C0, -0.5)
V12 = ( 0.0,  -C0,  0.5)
V13 = ( 0.0,  -C0, -0.5)
V14 = (  C1,   C1,   C1)
V15 = (  C1,   C1,  -C1)
V16 = ( -C1,  -C1,   C1)
V17 = ( -C1,  -C1,  -C1)
V18 = (  C0,  0.5,  0.0)
V19 = ( -C0, -0.5,  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 }