Biscribed Pentakis Dodecahedron with radius = 1

C0 = 0.356822089773089931941969843046 = (sqrt(15) - sqrt(3)) / 6
C1 = 0.525731112119133606025669084848 = sqrt(10 * (5 - sqrt(5))) / 10
C2 = 0.577350269189625764509148780502 = sqrt(3) / 3
C3 = 0.850650808352039932181540497063 = sqrt(10 * (5 + sqrt(5))) / 10
C4 = 0.934172358962715696451118623548 = (sqrt(3) + sqrt(15)) / 6

V0  = (0.0,  C0,  C4)
V1  = (0.0,  C0, -C4)
V2  = (0.0, -C0,  C4)
V3  = (0.0, -C0, -C4)
V4  = ( C4, 0.0,  C0)
V5  = ( C4, 0.0, -C0)
V6  = (-C4, 0.0,  C0)
V7  = (-C4, 0.0, -C0)
V8  = ( C0,  C4, 0.0)
V9  = ( C0, -C4, 0.0)
V10 = (-C0,  C4, 0.0)
V11 = (-C0, -C4, 0.0)
V12 = ( C1, 0.0,  C3)
V13 = ( C1, 0.0, -C3)
V14 = (-C1, 0.0,  C3)
V15 = (-C1, 0.0, -C3)
V16 = ( C3,  C1, 0.0)
V17 = ( C3, -C1, 0.0)
V18 = (-C3,  C1, 0.0)
V19 = (-C3, -C1, 0.0)
V20 = (0.0,  C3,  C1)
V21 = (0.0,  C3, -C1)
V22 = (0.0, -C3,  C1)
V23 = (0.0, -C3, -C1)
V24 = ( C2,  C2,  C2)
V25 = ( C2,  C2, -C2)
V26 = ( C2, -C2,  C2)
V27 = ( C2, -C2, -C2)
V28 = (-C2,  C2,  C2)
V29 = (-C2,  C2, -C2)
V30 = (-C2, -C2,  C2)
V31 = (-C2, -C2, -C2)

Faces:
{ 12,  0,  2 }
{ 12,  2, 26 }
{ 12, 26,  4 }
{ 12,  4, 24 }
{ 12, 24,  0 }
{ 13,  3,  1 }
{ 13,  1, 25 }
{ 13, 25,  5 }
{ 13,  5, 27 }
{ 13, 27,  3 }
{ 14,  2,  0 }
{ 14,  0, 28 }
{ 14, 28,  6 }
{ 14,  6, 30 }
{ 14, 30,  2 }
{ 15,  1,  3 }
{ 15,  3, 31 }
{ 15, 31,  7 }
{ 15,  7, 29 }
{ 15, 29,  1 }
{ 16,  4,  5 }
{ 16,  5, 25 }
{ 16, 25,  8 }
{ 16,  8, 24 }
{ 16, 24,  4 }
{ 17,  5,  4 }
{ 17,  4, 26 }
{ 17, 26,  9 }
{ 17,  9, 27 }
{ 17, 27,  5 }
{ 18,  7,  6 }
{ 18,  6, 28 }
{ 18, 28, 10 }
{ 18, 10, 29 }
{ 18, 29,  7 }
{ 19,  6,  7 }
{ 19,  7, 31 }
{ 19, 31, 11 }
{ 19, 11, 30 }
{ 19, 30,  6 }
{ 20,  8, 10 }
{ 20, 10, 28 }
{ 20, 28,  0 }
{ 20,  0, 24 }
{ 20, 24,  8 }
{ 21, 10,  8 }
{ 21,  8, 25 }
{ 21, 25,  1 }
{ 21,  1, 29 }
{ 21, 29, 10 }
{ 22, 11,  9 }
{ 22,  9, 26 }
{ 22, 26,  2 }
{ 22,  2, 30 }
{ 22, 30, 11 }
{ 23,  9, 11 }
{ 23, 11, 31 }
{ 23, 31,  3 }
{ 23,  3, 27 }
{ 23, 27,  9 }