Johnson Solids (Page 5)

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(J79) Bigyrate Diminished Rhombicosidodecahedron
Vertices:  55  ({2 * 5}[3] + {2 * 21 + 1 * 3}[4])
Faces:52  ({2 * 6 + 1 * 3} equilateral triangles
    + {2 * 11 + 1 * 3} squares + {2 * 4 + 1 * 3} regular pentagons
    + 1 regular decagon)
Edges:105
Symmetry:  Reflection  (Cs = C1h = C1v)
(values below based on edge length = 1)
Volume:(115+54*sqrt(5))/6    ≈39.291278464164773934