Self-Intersecting Snub Quasi-Regular Polyhedra

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(Uniform #64) Great Snub Dodecicosidodecahedron

Vertices:   60  (60[6]) Faces: 104  (80 equilateral triangles + 24 regular pentagrams) Edges: 180 Symmetry:   Chiral Icosahedral  (I) Pentagram-Triangle Angle 1:   acos(sqrt(15*(5+2*sqrt(5)         +4*sqrt(5*(sqrt(5)−2))))/15)     ≈16.303679801 degrees Triangle-Triangle Angle:   acos(−1/3)     ≈109.471220634 degrees Pentagram-Triangle Angle 2:   acos(−sqrt(15*(5+2*sqrt(5)         −4*sqrt(5*(sqrt(5)−2))))/15)     ≈125.7749004353 degrees Dual Solid:   Great Hexagonal Hexecontahedron (values below based on edge length = 1) Circumscribed Radius:   sqrt(2)/2     ≈0.70710678118654752440 Midscribed Radius:   1/2     0.5 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.