Johnson Solids (Page 1)

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(J3) Triangular Cupola
Vertices:  9  (6[3] + 3[4])
Faces:8  ({3 + 1} equilateral triangles + 3 squares + 1 regular hexagon)
Edges:15
Symmetry:  3-fold Pyramidal  (C3v)
(values below based on edge length = 1)
Volume:5*sqrt(2)/6    ≈1.1785113019775792073