Tridyakis Icosahedron

C0 = 0.772542485937368560255733542957 = 5 * (sqrt(5) - 1) / 8
C1 = 1.03647450843757886384655987423  = 3 * (5 - sqrt(5)) / 8
C2 = 1.677050983124842272306880251548 = 3 * sqrt(5) / 4
C3 = 2.02254248593736856025573354296  = 5 * (1 + sqrt(5)) / 8
C4 = 2.71352549156242113615344012577  = 3 * (5 + sqrt(5)) / 8

V0  = (   C2,   0.0,    C4)
V1  = (   C2,   0.0,   -C4)
V2  = (  -C2,   0.0,    C4)
V3  = (  -C2,   0.0,   -C4)
V4  = (   C4,    C2,   0.0)
V5  = (   C4,   -C2,   0.0)
V6  = (  -C4,    C2,   0.0)
V7  = (  -C4,   -C2,   0.0)
V8  = (  0.0,    C4,    C2)
V9  = (  0.0,    C4,   -C2)
V10 = (  0.0,   -C4,    C2)
V11 = (  0.0,   -C4,   -C2)
V12 = (  0.0,    C0,    C3)
V13 = (  0.0,    C0,   -C3)
V14 = (  0.0,   -C0,    C3)
V15 = (  0.0,   -C0,   -C3)
V16 = (   C3,   0.0,    C0)
V17 = (   C3,   0.0,   -C0)
V18 = (  -C3,   0.0,    C0)
V19 = (  -C3,   0.0,   -C0)
V20 = (   C0,    C3,   0.0)
V21 = (   C0,   -C3,   0.0)
V22 = (  -C0,    C3,   0.0)
V23 = (  -C0,   -C3,   0.0)
V24 = (   C1,   0.0,    C2)
V25 = (   C1,   0.0,   -C2)
V26 = (  -C1,   0.0,    C2)
V27 = (  -C1,   0.0,   -C2)
V28 = (   C2,    C1,   0.0)
V29 = (   C2,   -C1,   0.0)
V30 = (  -C2,    C1,   0.0)
V31 = (  -C2,   -C1,   0.0)
V32 = (  0.0,    C2,    C1)
V33 = (  0.0,    C2,   -C1)
V34 = (  0.0,   -C2,    C1)
V35 = (  0.0,   -C2,   -C1)
V36 = ( 1.25,  1.25,  1.25)
V37 = ( 1.25,  1.25, -1.25)
V38 = ( 1.25, -1.25,  1.25)
V39 = ( 1.25, -1.25, -1.25)
V40 = (-1.25,  1.25,  1.25)
V41 = (-1.25,  1.25, -1.25)
V42 = (-1.25, -1.25,  1.25)
V43 = (-1.25, -1.25, -1.25)

Faces:
{  0, 17, 28 }
{  0, 28, 20 }
{  0, 20, 32 }
{  0, 32, 40 }
{  0, 40, 26 }
{  0, 26, 42 }
{  0, 42, 34 }
{  0, 34, 21 }
{  0, 21, 29 }
{  0, 29, 17 }
{  1, 16, 29 }
{  1, 29, 21 }
{  1, 21, 35 }
{  1, 35, 43 }
{  1, 43, 27 }
{  1, 27, 41 }
{  1, 41, 33 }
{  1, 33, 20 }
{  1, 20, 28 }
{  1, 28, 16 }
{  2, 19, 31 }
{  2, 31, 23 }
{  2, 23, 34 }
{  2, 34, 38 }
{  2, 38, 24 }
{  2, 24, 36 }
{  2, 36, 32 }
{  2, 32, 22 }
{  2, 22, 30 }
{  2, 30, 19 }
{  3, 18, 30 }
{  3, 30, 22 }
{  3, 22, 33 }
{  3, 33, 37 }
{  3, 37, 25 }
{  3, 25, 39 }
{  3, 39, 35 }
{  3, 35, 23 }
{  3, 23, 31 }
{  3, 31, 18 }
{  4, 12, 24 }
{  4, 24, 38 }
{  4, 38, 29 }
{  4, 29, 39 }
{  4, 39, 25 }
{  4, 25, 13 }
{  4, 13, 33 }
{  4, 33, 22 }
{  4, 22, 32 }
{  4, 32, 12 }
{  5, 14, 34 }
{  5, 34, 23 }
{  5, 23, 35 }
{  5, 35, 15 }
{  5, 15, 25 }
{  5, 25, 37 }
{  5, 37, 28 }
{  5, 28, 36 }
{  5, 36, 24 }
{  5, 24, 14 }
{  6, 12, 32 }
{  6, 32, 20 }
{  6, 20, 33 }
{  6, 33, 13 }
{  6, 13, 27 }
{  6, 27, 43 }
{  6, 43, 31 }
{  6, 31, 42 }
{  6, 42, 26 }
{  6, 26, 12 }
{  7, 14, 26 }
{  7, 26, 40 }
{  7, 40, 30 }
{  7, 30, 41 }
{  7, 41, 27 }
{  7, 27, 15 }
{  7, 15, 35 }
{  7, 35, 21 }
{  7, 21, 34 }
{  7, 34, 14 }
{  8, 14, 24 }
{  8, 24, 16 }
{  8, 16, 28 }
{  8, 28, 37 }
{  8, 37, 33 }
{  8, 33, 41 }
{  8, 41, 30 }
{  8, 30, 18 }
{  8, 18, 26 }
{  8, 26, 14 }
{  9, 15, 27 }
{  9, 27, 19 }
{  9, 19, 30 }
{  9, 30, 40 }
{  9, 40, 32 }
{  9, 32, 36 }
{  9, 36, 28 }
{  9, 28, 17 }
{  9, 17, 25 }
{  9, 25, 15 }
{ 10, 12, 26 }
{ 10, 26, 18 }
{ 10, 18, 31 }
{ 10, 31, 43 }
{ 10, 43, 35 }
{ 10, 35, 39 }
{ 10, 39, 29 }
{ 10, 29, 16 }
{ 10, 16, 24 }
{ 10, 24, 12 }
{ 11, 13, 25 }
{ 11, 25, 17 }
{ 11, 17, 29 }
{ 11, 29, 38 }
{ 11, 38, 34 }
{ 11, 34, 42 }
{ 11, 42, 31 }
{ 11, 31, 19 }
{ 11, 19, 27 }
{ 11, 27, 13 }