Square Antiprism-Trapezohedron Toroid

C0 = 0.0721375078778507478291882437893 = sqrt(2 * (17 * sqrt(2) - 24)) / 4
C1 = 0.112085382291991279528598381347  = sqrt(2 * (10 - 7 * sqrt(2))) / 4
C2 = 0.270598050073098492199861602683  = sqrt(2 * (2 - sqrt(2))) / 4
C3 = 0.420448207626857271515562738117  = sqrt(2 * sqrt(2)) / 4
C4 = 0.653281482438188263928321586714  = sqrt(2 * (2 + sqrt(2))) / 4

V0  = ( C4,  C2,  C3)
V1  = ( C4, -C2, -C3)
V2  = (-C4, -C2,  C3)
V3  = (-C4,  C2, -C3)
V4  = ( C2, -C4,  C3)
V5  = ( C2,  C4, -C3)
V6  = (-C2,  C4,  C3)
V7  = (-C2, -C4, -C3)
V8  = ( C2, -C1,  C0)
V9  = ( C2,  C1, -C0)
V10 = (-C2,  C1,  C0)
V11 = (-C2, -C1, -C0)
V12 = ( C1,  C2,  C0)
V13 = ( C1, -C2, -C0)
V14 = (-C1, -C2,  C0)
V15 = (-C1,  C2, -C0)

Faces:
{  0,  6, 15, 12,  9 }
{  0,  9,  8, 13,  4 }
{  1,  7, 14, 13,  8 }
{  1,  8,  9, 12,  5 }
{  2,  4, 13, 14, 11 }
{  2, 11, 10, 15,  6 }
{  3,  5, 12, 15, 10 }
{  3, 10, 11, 14,  7 }
{  0,  4,  1 }
{  0,  1,  5 }
{  2,  6,  3 }
{  2,  3,  7 }
{  4,  2,  7 }
{  4,  7,  1 }
{  6,  0,  5 }
{  6,  5,  3 }