Pentagrammic Dipyramid

C0 = 0.525731112119133606025669084848 = sqrt(10 * (5 - sqrt(5))) / 10
C1 = 0.552786404500042060718165266254 = (5 - sqrt(5)) / 5
C2 = 1.37638192047117353820720958191  = sqrt(5 * (5 + 2 * sqrt(5))) / 5
C3 = 1.61803398874989484820458683437  = (1 + sqrt(5)) / 2
C4 = 1.70130161670407986436308099413  = sqrt(10 * (5 + sqrt(5))) / 5

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

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