Self-Dual Decahedron #12 (canonical)

C0 = 0.227544930281113670652178878911 = sqrt(2 * (sqrt(2) - 1)) / 4
C1 = 0.414213562373095048801688724210 = sqrt(2) - 1
C2 = 0.643594252905582624735443437418 = sqrt(sqrt(2) - 1)
C3 = 0.754017569373421133724342718383 = 2 * sqrt(2 * (5 * sqrt(2) - 7))
C4 = 0.757359312880714853594933827371 = 5 - 3 * sqrt(2)
C5 = 1.28718850581116524947088687484  = 2 * sqrt(sqrt(2) - 1)

V0 = ( C0, -C0,  1.0)
V1 = (-C0,  C0,  1.0)
V2 = (0.0,  C2, -1.0)
V3 = (0.0, -C2, -1.0)
V4 = ( C3, 0.0,  -C4)
V5 = (-C3, 0.0,  -C4)
V6 = ( C5, 0.0,   C1)
V7 = (-C5, 0.0,   C1)
V8 = (0.0,  C5,   C1)
V9 = (0.0, -C5,   C1)

Faces:
{ 6, 9, 3, 4 }
{ 6, 4, 2, 8 }
{ 6, 8, 1, 0 }
{ 7, 8, 2, 5 }
{ 7, 5, 3, 9 }
{ 7, 9, 0, 1 }
{ 2, 4, 3 }
{ 2, 3, 5 }
{ 0, 9, 6 }
{ 1, 8, 7 }
