Johnson Solids (Page 1)

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(J5) Pentagonal Cupola
Vertices:  15  (10[3] + 5[4])
Faces:12  (5 equilateral triangles + 5 squares + 1 regular pentagon
    + 1 regular decagon)
Edges:25
Symmetry:  5-fold Pyramidal  (C5v)
(values below based on edge length = 1)
Volume:(5+4*sqrt(5))/6    ≈2.3240453183331931309