Pentagrammic Trapezohedron

C0 = 0.162459848116453163077935706108 = sqrt(5 * (5 - 2 * sqrt(5))) / 10
C1 = 0.242934135878322839091431937947 = sqrt(sqrt(5) - 2) / 2
C2 = 0.309016994374947424102293417183 = (sqrt(5) - 1) / 4
C3 = 0.425325404176019966090770248532 = sqrt(10 * (5 + sqrt(5))) / 20
C4 = 0.460221032629963017882682597106 = sqrt(5 * (2 + sqrt(5))) / 10
C5 = 0.525731112119133606025669084848 = sqrt(10 * (5 - sqrt(5))) / 10

V0  = (  C2,  C3, -C1)
V1  = ( -C2,  C3, -C1)
V2  = ( -C2,  C3,  C1)
V3  = (  C2,  C3,  C1)
V4  = ( 0.5, -C0,  C1)
V5  = (-0.5, -C0,  C1)
V6  = (-0.5, -C0, -C1)
V7  = ( 0.5, -C0, -C1)
V8  = ( 0.0, 0.0,  C4)
V9  = ( 0.0, 0.0, -C4)
V10 = ( 0.0, -C5, -C1)
V11 = ( 0.0, -C5,  C1)

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