Self-Intersecting Quasi-Quasi-Regular Polyhedra

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(Uniform #43) Small Ditrigonal Dodecicosidodecahedron

Vertices:   60  (60[4]) Faces: 44  (20 equilateral triangles + 12 regular pentagrams     + 12 regular decagons) Edges: 120 Symmetry:   Full Icosahedral  (Ih) Decagon-Triangle Angle:   acos(−sqrt(15*(5−2*sqrt(5)))/15)     ≈100.812316964 degrees Decagon-Pentagram Angle:   acos(sqrt(5)/5)     ≈296.565051177 degrees Dual Solid:   Small Ditrigonal Dodecacronic Hexecontahedron (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 Triangle Center Radius:   (9*sqrt(3)+sqrt(15))/12     ≈1.6217867178606093772 Pentagram Center Radius:   sqrt(10*(65+19*sqrt(5)))/20     ≈1.6392474765307403412 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.