Elongated Square Dipyramid

C0 = 1.20710678118654752440084436210 = (1 + sqrt(2)) / 2

V0 = ( 0.5,  0.5,  0.5)
V1 = ( 0.5,  0.5, -0.5)
V2 = ( 0.5, -0.5,  0.5)
V3 = ( 0.5, -0.5, -0.5)
V4 = (-0.5,  0.5,  0.5)
V5 = (-0.5,  0.5, -0.5)
V6 = (-0.5, -0.5,  0.5)
V7 = (-0.5, -0.5, -0.5)
V8 = ( 0.0,  0.0,   C0)
V9 = ( 0.0,  0.0,  -C0)

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