Versi-Quasi-Regular Polyhedra

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(Uniform #50) Small Dodecicosahedron
Vertices:  60  (60[4])
Faces:32  (20 regular hexagons + 12 regular decagons)
Edges:120
Symmetry:  Full Icosahedral  (Ih)
Dihedral Angle 1 (60):  acos(sqrt(15*(5+2*sqrt(5)))/15)    ≈37.377368141 degrees
Dihedral Angle 2 (60):  acos(sqrt(15*(5−2*sqrt(5)))/15)    ≈79.187683036 degrees
Dual Solid:  Small Dodecicosacron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(2*(17+3*sqrt(5)))/4    ≈1.7214893236852853443
Midscribed Radius:  sqrt(6*(5+sqrt(5)))/4    ≈1.6472782070926638518
Decagon Center Radius:  sqrt(2*(5−sqrt(5)))/4    ≈0.58778525229247312917
Hexagon Center Radius:  (sqrt(3)+sqrt(15))/4    ≈1.4012585384440735447


References:[1]H. S. M. Coxeter, M. S. Longuet-Higgins, and J. C. P. Miller,
Uniform Polyhedra, Philosophical Transactions of the Royal Society of London.
Series A. Mathematical and Physical Sciences 246 (1954), 401-450.