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.