Pentakis Icosidodecahedron (canonical)

C0 = 0.3249196962329063261558714122151
C1 = 0.525731112119133606025669084848
C2 = 0.541166900871121200823328817258
C3 = 0.850650808352039932181540497063
C4 = 0.875626439195919181581615733217
C5 = 1.05146222423826721205133816970

C0 = sqrt(5 * (5 - 2 * sqrt(5))) / 5
C1 = sqrt(10 * (5 - sqrt(5))) / 10
C2 = (6 * sqrt(5) + sqrt(2 * (85 - sqrt(5))) - 16) / 19
C3 = sqrt(10 * (5 + sqrt(5))) / 10
C4 = (7 - 5 * sqrt(5) + sqrt(2 * (125 + 41 * sqrt(5)))) / 19
C5 = sqrt(10 * (5 - sqrt(5))) / 5

V0  = (0.0, 0.0,  C5)
V1  = (0.0, 0.0, -C5)
V2  = ( C5, 0.0, 0.0)
V3  = (-C5, 0.0, 0.0)
V4  = (0.0,  C5, 0.0)
V5  = (0.0, -C5, 0.0)
V6  = ( C2, 0.0,  C4)
V7  = ( C2, 0.0, -C4)
V8  = (-C2, 0.0,  C4)
V9  = (-C2, 0.0, -C4)
V10 = ( C4,  C2, 0.0)
V11 = ( C4, -C2, 0.0)
V12 = (-C4,  C2, 0.0)
V13 = (-C4, -C2, 0.0)
V14 = (0.0,  C4,  C2)
V15 = (0.0,  C4, -C2)
V16 = (0.0, -C4,  C2)
V17 = (0.0, -C4, -C2)
V18 = ( C0,  C1,  C3)
V19 = ( C0,  C1, -C3)
V20 = ( C0, -C1,  C3)
V21 = ( C0, -C1, -C3)
V22 = (-C0,  C1,  C3)
V23 = (-C0,  C1, -C3)
V24 = (-C0, -C1,  C3)
V25 = (-C0, -C1, -C3)
V26 = ( C3,  C0,  C1)
V27 = ( C3,  C0, -C1)
V28 = ( C3, -C0,  C1)
V29 = ( C3, -C0, -C1)
V30 = (-C3,  C0,  C1)
V31 = (-C3,  C0, -C1)
V32 = (-C3, -C0,  C1)
V33 = (-C3, -C0, -C1)
V34 = ( C1,  C3,  C0)
V35 = ( C1,  C3, -C0)
V36 = ( C1, -C3,  C0)
V37 = ( C1, -C3, -C0)
V38 = (-C1,  C3,  C0)
V39 = (-C1,  C3, -C0)
V40 = (-C1, -C3,  C0)
V41 = (-C1, -C3, -C0)

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