Truncated Archimedean Solids

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Canonical Truncated Rhombicosidodecahedron
canonical form
Vertices:  240  (120[3] + 120[3])
Faces:122  (12 regular decagons + 30 bi-mirror-symmetric octagons
    + 20 regular hexagons + 60 isosceles trapezoids)
Edges:360  (120 short + 120 medium + 120 long)
Symmetry:  Full Icosahedral  (Ih)
(values below based on edge-scribed radius = 1)
Short Edge (120):  sqrt(5*(95−31*sqrt(5)    
    −sqrt(10*(33+5*sqrt(5)))))/30    
≈0.16094810856075452707
Medium Edge (120):  sqrt(10*(349−137*sqrt(5)    
    −sqrt(2*(61233−27179*sqrt(5)))))/60    
≈0.185316503761267669951
Long Edge (120):  sqrt(15*(111−47*sqrt(5)    
    −sqrt(2*(10933−4887*sqrt(5)))))/30    
≈0.20968489896178081283
Edge-scribed Radius:  1
Volume:sqrt(2*(141149−62360*sqrt(5)    
    +sqrt(8980284291    
    −4015739612*sqrt(5))))/18    
≈4.0153865725314955596