Rectified Archimedean Solids

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Canonical Rectified Truncated Icosahedron
canonical form
Vertices:  90  (60[4] + 30[4])
Faces:92  (20 triambi + 12 regular pentagons + 60 isosceles triangles)
Edges:180  (60 short + 120 long)
Symmetry:  Full Icosahedral  (Ih)
(values below based on edge-scribed radius = 1)
Short Edge (60):  sqrt(root[8th-order polynomial])    ≈0.34561036856829377206
Long Edge (120):  sqrt(root[8th-order polynomial])    ≈0.35955500694389121026
Edge-scribed Radius:  1
Volume:sqrt(root[8th-order polynomial])    ≈4.0095940519753525228