Johnson Solids (Page 1)

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(J4) Square Cupola
Vertices:  12  (8[3] + 4[4])
Faces:10  (4 equilateral triangles + {4 + 1} squares + 1 regular octagon)
Edges:20
Symmetry:  4-fold Pyramidal  (C4v)
(values below based on edge length = 1)
Volume:(3+2*sqrt(2))/3    ≈1.9428090415820633659