Self-Intersecting Quasi-Regular Polyhedra

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(Uniform #54) Great Icosidodecahedron

Vertices:   30  (30[4]) Faces: 32  (20 equilateral triangles + 12 regular pentagrams) Edges: 60 Symmetry:   Full Icosahedral  (Ih) Dihedral Angle:   acos(−sqrt(15*(5−2*sqrt(5)))/15)     ≈100.812316964 degrees Dual Solid:   Great Rhombic Triacontahedron (values below based on edge length = 1) Circumscribed Radius:   (sqrt(5)−1)/2     ≈0.61803398874989484820 Midscribed Radius:   sqrt(5−2*sqrt(5))/2     ≈0.363271264002680442948 Triangle Center Radius:   (3*sqrt(3)−sqrt(15))/6     ≈0.22052817941653583257 Pentagram Center Radius:   sqrt(5*(5−2*sqrt(5)))/5     ≈0.32491969623290632616 References: [1] Edmund Hess, Über vier Archimedeische Polyeder höherer Art, Schriften der Gesellschaft zur Beförderung der gesammten Naturwissenschaften zu Marburg 11(4) (1878). [2] Jean Paul Albert Badoureau, Mémoire sur les Figures Isocèles, Journal de l'École polytechnique 49 (1881), 47-172. [3] Johann Pitsch, Über Halbreguläre Sternpolyeder, Zeitschrift für das Realschulwesen 6 (1881), 9-24, 64-65, 72-89, 216.