Johnson Solids (Page 1)

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(J17) Gyroelongated Square Dipyramid
Vertices:  10  (2[4] + 8[5])
Faces:16  ({8 * 2} equilateral triangles)
Edges:24
Symmetry:  4-fold Antiprismatic  (D4v)
(values below based on edge length = 1)
Volume:(sqrt(2)+sqrt(4+3*sqrt(2)))/3    ≈1.42840450262774840053