Johnson Solids (Page 5)

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(J87) Augmented Sphenocorona
Vertices:  11  ({2 + 1}[4] + {2 * 3 + 1 * 2}[5])
Faces:17  ({2 * 6 + 1 * 4} equilateral triangles + 1 square)
Edges:26
Symmetry:  Reflection  (Cs = C1h = C1v)
(values below based on edge length = 1)
Volume:(2*sqrt(2)+3*sqrt(2*(2+3*sqrt(6)    
    +2*sqrt(13+3*sqrt(6)))))/12    
≈1.7510539003719224012