Johnson Solids (Page 2)

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(J28) Square Orthobicupola
Vertices:  16  ({8 * 2}[4])
Faces:18  (8 equilateral triangles + {8 + 2} squares)
Edges:32
Symmetry:  4-fold Prismatic  (D4h)
(values below based on edge length = 1)
Volume:(6+4*sqrt(2))/3    ≈3.8856180831641267317