Johnson Solids (Page 4)

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(J76) Diminished Rhombicosidodecahedron
Vertices:  55  (10[3] + {10 * 3 + 5 * 3}[4])
Faces:52  ({5 * 3} equilateral triangles + {10 + 5 * 3} squares
    + {5 * 2 + 1} regular pentagons + 1 regular decagon)
Edges:105
Symmetry:  5-fold Pyramidal  (C5v)
(values below based on edge length = 1)
Volume:(115+54*sqrt(5))/6    ≈39.291278464164773934