Triakis Tetrahedron

C0 = 0.636396103067892771960759925894 = 9 * sqrt(2) / 20
C1 = 1.06066017177982128660126654316  = 3 * sqrt(2) / 4

V0 = ( C1,  C1,  C1)
V1 = ( C1, -C1, -C1)
V2 = (-C1, -C1,  C1)
V3 = (-C1,  C1, -C1)
V4 = ( C0, -C0,  C0)
V5 = ( C0,  C0, -C0)
V6 = (-C0,  C0,  C0)
V7 = (-C0, -C0, -C0)

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