Self-Dual Enneahedron #8 (canonical)

C0  = 0.108306565410968775385290470738  = sqrt(5 * (5 - 2 * sqrt(5))) / 15
C1  = 0.171513425153809858988423546114  = sqrt(85 - 38 * sqrt(5))
C2  = 0.307290076312131951938212140752  = sqrt(10 * (sqrt(5) - 2)) / 5
C3  = 0.3249196962329063261558714122151 = sqrt(5 * (5 - 2 * sqrt(5))) / 5
C4  = 0.361241150064199600417507179802  = sqrt(5 * (7 * sqrt(5) - 15)) / 5
C5  = 0.687121499445024928277131487829  = sqrt(2 * (sqrt(5) - 2))
C6  = 0.945741609003175813301696119887  = sqrt(10 * sqrt(5)) / 5
C7  = 0.998445982507245176736665198643  = 2 * sqrt(2 * (9 * sqrt(5) - 20))
C8  = 1.02016137862810135079059003998   = 2 * sqrt(5 * (5 + 3 * sqrt(5))) / 15
C9  = 1.11178594050284234398409609580   = sqrt(sqrt(5) - 1)
C10 = 3.07768353717525340257029057604   = sqrt(5 + 2 * sqrt(5))

V0 = ( C9,  C4, -C3)
V1 = (-C9,  C4, -C3)
V2 = ( C5, -C6, -C3)
V3 = (-C5, -C6, -C3)
V4 = ( C2,  C6, -C3)
V5 = (-C2,  C6, -C3)
V6 = (0.0, 0.0, C10)
V7 = (0.0, -C7,  C1)
V8 = (0.0,  C8,  C0)

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