Square Antiprism

C0 = 0.420448207626857271515562738117  = sqrt(2 * sqrt(2)) / 4
C1 = 0.7071067811865475244008443621048 = sqrt(2) / 2

V0 = ( 0.5,  0.5,  C0)
V1 = ( 0.5, -0.5,  C0)
V2 = (-0.5,  0.5,  C0)
V3 = (-0.5, -0.5,  C0)
V4 = (  C1,  0.0, -C0)
V5 = ( -C1,  0.0, -C0)
V6 = ( 0.0,   C1, -C0)
V7 = ( 0.0,  -C1, -C0)

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