Self-Dual Enneahedron #3 (canonical)

C0 = 0.414213562373095048801688724210 = sqrt(2) - 1
C1 = 0.703986770044140568557964133917 = 2 * sqrt(5 * sqrt(2) - 1) / 7
C2 = 0.867295401695067892001206231578 = (5 * sqrt(2) - 1) / 7
C3 = 1.15300968740935360628692051729  = (1 + 5 * sqrt(2)) / 7
C4 = 1.28718850581116524947088687484  = 2 * sqrt(sqrt(2) - 1)

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

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