Pentagonal Trapezohedron Toroid

C0  = 0.161803398874989484820458683437 = (1 + sqrt(5)) / 20
C1  = 0.190983005625052575897706582817 = (3 - sqrt(5)) / 4
C2  = 0.261803398874989484820458683437 = (3 + sqrt(5)) / 20
C3  = 0.309016994374947424102293417183 = (sqrt(5) - 1) / 4
C4  = 0.323606797749978969640917366873 = (1 + sqrt(5)) / 10
C5  = 0.585410196624968454461376050310 = (5 + 3 * sqrt(5)) / 20
C6  = 0.685410196624968454461376050310 = (7 + 3 * sqrt(5)) / 20
C7  = 0.747213595499957939281834733746 = (3 + 2 * sqrt(5)) / 10
C8  = 0.785410196624968454461376050310 = 3 * (3 + sqrt(5)) / 20
C9  = 0.809016994374947424102293417183 = (1 + sqrt(5)) / 4
C10 = 0.947213595499957939281834733746 = (5 + 2 * sqrt(5)) / 10

V0  = (  C4,   C0,  C10)
V1  = (  C4,   C0, -C10)
V2  = ( -C4,  -C0,  C10)
V3  = ( -C4,  -C0, -C10)
V4  = ( 0.5,  0.0,   C9)
V5  = ( 0.5,  0.0,  -C9)
V6  = (-0.5,  0.0,   C9)
V7  = (-0.5,  0.0,  -C9)
V8  = (  C9,  0.5,  0.0)
V9  = ( -C9, -0.5,  0.0)
V10 = ( 0.0,   C9,  0.5)
V11 = ( 0.0,   C9, -0.5)
V12 = ( 0.0,  -C9,  0.5)
V13 = ( 0.0,  -C9, -0.5)
V14 = (  C2,   C8,   C5)
V15 = (  C2,   C8,  -C5)
V16 = ( -C2,  -C8,   C5)
V17 = ( -C2,  -C8,  -C5)
V18 = ( 0.0,   C1,  0.5)
V19 = ( 0.0,   C1, -0.5)
V20 = ( 0.0,  -C1,  0.5)
V21 = ( 0.0,  -C1, -0.5)
V22 = (  C1,  0.5,  0.0)
V23 = ( -C1, -0.5,  0.0)
V24 = (  C3,   C3,   C3)
V25 = (  C3,   C3,  -C3)
V26 = ( -C3,  -C3,   C3)
V27 = ( -C3,  -C3,  -C3)
V28 = (  C6,   C7,  0.0)
V29 = ( -C6,  -C7,  0.0)

Faces:
{  4, 12, 26, 20, 18 }
{  4, 18, 24, 22,  8 }
{  4,  0,  2, 16, 12 }
{  4,  8, 28, 14,  0 }
{  5, 19, 21, 27, 13 }
{  5,  8, 22, 25, 19 }
{  5,  1, 15, 28,  8 }
{  5, 13, 17,  3,  1 }
{  6, 10, 24, 18, 20 }
{  6, 20, 26, 23,  9 }
{  6,  9, 29, 16,  2 }
{  6,  2,  0, 14, 10 }
{  7,  9, 23, 27, 21 }
{  7, 21, 19, 25, 11 }
{  7, 11, 15,  1,  3 }
{  7,  3, 17, 29,  9 }
{ 10, 11, 25, 22, 24 }
{ 10, 14, 28, 15, 11 }
{ 12, 13, 27, 23, 26 }
{ 12, 16, 29, 17, 13 }