Archimedean Solids

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(Uniform #27) Rhombicosidodecahedron
Vertices:  60  (60[4])
Faces:62  (20 equilateral triangles + 30 squares + 12 regular pentagons)
Edges:120
Symmetry:  Full Icosahedral  (Ih)
Pentagon-Square Angle:  acos(−sqrt(10*(5+sqrt(5)))/10)    ≈148.282525589 degrees
Square-Triangle Angle:  acos(−(sqrt(3)+sqrt(15))/6)    ≈159.094842552 degrees
Dual Solid:  Deltoidal Hexecontahedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(11+4*sqrt(5))/2    ≈2.2329505094156900495004
Midscribed Radius:  sqrt(2*(5+2*sqrt(5)))/2    ≈2.1762508994828215111
Pentagon Center Radius:  3*sqrt(5*(5+2*sqrt(5)))/10    ≈2.0645728807067603073
Square Center Radius:  (2+sqrt(5))/2    ≈2.1180339887498948482
Triangle Center Radius:  (3*sqrt(3)+2*sqrt(15))/6    ≈2.1570198525202442752
Volume:(60+29*sqrt(5))/3    ≈41.6153237824979670653