Self-Intersecting Snub Quasi-Regular Polyhedra

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(Uniform #75) Great Dirhombicosidodecahedron

Vertices:   60  (60[8]) Faces: 124  (40 equilateral triangles + 60 squares + 24 regular pentagrams) Edges: 240 Symmetry:   Full Icosahedral  (Ih) Square-Triangle Angle:   acos(sqrt(3)/3)     ≈54.735610317 degrees Pentagram-Square Angle:   acos(sqrt(5*(5−2*sqrt(5)))/5)     ≈71.039290118 degrees Dual Solid:   Great Dirhombicosidodecacron (values below based on edge length = 1) Circumscribed Radius:   sqrt(2)/2     ≈0.70710678118654752440 Midscribed Radius:   1/2     0.5 Square Center Radius:   0 Triangle Center Radius:   sqrt(6)/6     ≈0.40824829046386301637 Pentagram Center Radius:   sqrt(10*sqrt(5))/10     ≈0.472870804501587906651 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.