Rectified Archimedean Solids

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Rectified Truncated Icosahedron
derived form
Vertices:  90  (30[4] + 60[4])
Faces:92  (20 regular hexagons + 12 regular pentagons
    + 60 isosceles triangles)
Edges:180  (60 short + 120 long)
Symmetry:  Full Icosahedral  (Ih)
(values below based on short edge length = 1)
Short Edge (60):  1
Long Edge (120):  (sqrt(15)−sqrt(3))/2    ≈1.0704662693192697958
Circumscribed Radius:  3
Volume:73*sqrt(5)−60    ≈103.23296235748464784