Johnson Solids (Page 2)

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(J33) Pentagonal Gyrocupolarotunda
Vertices:  25  ({10 + 5 * 3}[4])
Faces:27  ({5 * 3} equilateral triangles + 5 squares
    + {5 + 1 * 2} regular pentagons)
Edges:50
Symmetry:  5-fold Pyramidal  (C5v)
(values below based on edge length = 1)
Volume:(55+25*sqrt(5))/12    ≈9.2418082864578952009