Rhombic Icosahedron

C0 = 0.100405707943113639934898836316 = sqrt(10 * (25 - 11 * sqrt(5))) / 20
C1 = 0.262865556059566803012834542424 = sqrt(10 * (5 - sqrt(5))) / 20
C2 = 0.425325404176019966090770248532 = sqrt(10 * (5 + sqrt(5))) / 20
C3 = 0.525731112119133606025669084848 = sqrt(10 * (5 - sqrt(5))) / 10
C4 = 0.587785252292473129168705954639 = sqrt(2 * (5 - sqrt(5))) / 4
C5 = 0.850650808352039932181540497063 = sqrt(10 * (5 + sqrt(5))) / 10
C6 = 0.951056516295153572116439333379 = sqrt(2 * (5 + sqrt(5))) / 4
C7 = 1.11351636441160673519437503949  = sqrt(10 * (25 + 11 * sqrt(5))) / 20
C8 = 1.37638192047117353820720958191  = sqrt(5 * (5 + 2 * sqrt(5))) / 5

V0  = ( C2, -C1,  C8)
V1  = ( C2, -C1, -C8)
V2  = (-C2,  C1,  C8)
V3  = (-C2,  C1, -C8)
V4  = ( C2, -C7,  C5)
V5  = ( C2, -C7, -C5)
V6  = (-C2,  C7,  C5)
V7  = (-C2,  C7, -C5)
V8  = ( C2,  C4,  C5)
V9  = ( C2,  C4, -C5)
V10 = (-C2, -C4,  C5)
V11 = (-C2, -C4, -C5)
V12 = ( C6, -C1,  C3)
V13 = ( C6, -C1, -C3)
V14 = (-C6,  C1,  C3)
V15 = (-C6,  C1, -C3)
V16 = ( C6, -C7, 0.0)
V17 = (-C6,  C7, 0.0)
V18 = ( C6,  C4, 0.0)
V19 = (-C6, -C4, 0.0)
V20 = ( C0,  C7, 0.0)
V21 = (-C0, -C7, 0.0)

Faces:
{ 18,  8,  0, 12 }
{ 18, 12, 16, 13 }
{ 18, 13,  1,  9 }
{ 18,  9,  7, 20 }
{ 18, 20,  6,  8 }
{ 19, 10,  2, 14 }
{ 19, 14, 17, 15 }
{ 19, 15,  3, 11 }
{ 19, 11,  5, 21 }
{ 19, 21,  4, 10 }
{  8,  6,  2,  0 }
{  9,  1,  3,  7 }
{ 10,  4,  0,  2 }
{ 11,  3,  1,  5 }
{ 12,  0,  4, 16 }
{ 13, 16,  5,  1 }
{ 14,  2,  6, 17 }
{ 15, 17,  7,  3 }
{ 20,  7, 17,  6 }
{ 21,  5, 16,  4 }