Self-Dual Dodecahedron #5 (canonical)

C0 = 0.382683432365089771728459984030 = sqrt(2 - sqrt(2)) / 2
C1 = 0.414213562373095048801688724210 = sqrt(2) - 1
C2 = 0.541196100146196984399723205366 = sqrt(2 * (2 - sqrt(2))) / 2
C3 = 0.765366864730179543456919968061 = sqrt(2 - sqrt(2))
C4 = 0.923879532511286756128183189397 = sqrt(2 + sqrt(2)) / 2
C5 = 1.30656296487637652785664317343  = sqrt(2 * (2 + sqrt(2))) / 2

V0  = ( 0.0, -C0,  C5)
V1  = ( 0.0,  C0, -C5)
V2  = (  C1,  C2,  C3)
V3  = (  C1, -C2, -C3)
V4  = ( -C1,  C2,  C3)
V5  = ( -C1, -C2, -C3)
V6  = ( 0.0,  C4,  C2)
V7  = ( 0.0, -C4, -C2)
V8  = ( 1.0,  C3, 0.0)
V9  = ( 1.0, -C3, 0.0)
V10 = (-1.0,  C3, 0.0)
V11 = (-1.0, -C3, 0.0)

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