Rectified Archimedean Solids

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Rectified Truncated Icosidodecahedron
derived form
Vertices:  180  (60[4] + 60[4] + 60[4])
Faces:182  (12 regular decagons + 20 regular hexagons
    + 30 squares + {60 * 2} acute triangles)
Edges:360  (120 short + 120 medium + 120 long)
Symmetry:  Full Icosahedral  (Ih)
(values below based on short edge length = 1)
Short Edge (120):  1
Medium Edge (120):  sqrt(6)/2    ≈1.2247448713915890491
Long Edge (120):  sqrt(5+sqrt(5))/2    ≈1.3449970239279146539
Circumscribed Radius:  sqrt(3*(5+2*sqrt(5)))    ≈5.3307042560058364373
Volume:5*(153*sqrt(2)+79*sqrt(10))/4    ≈582.74326274548188712