Johnson Solids (Page 4)

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(J62) Metabidiminished Icosahedron
Vertices:  10  (2[3] + {4 + 2}[4] + 2[5])
Faces:12  ({4 + 2 * 3} equilateral triangles + 2 regular pentagons)
Edges:20
Symmetry:  2-fold Pyramidal  (C2v)
(values below based on edge length = 1)
Volume:(5+2*sqrt(5))/6    ≈1.5786893258332632321