Self-Intersecting Quasi-Quasi-Regular Polyhedra

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(Uniform #48) Great Icosicosidodecahedron
Vertices:  60  (60[4])
Faces:52  (20 equilateral triangles + 12 regular pentagons
    + 20 regular hexagons)
Edges:120
Symmetry:  Full Icosahedral  (Ih)
Hexagon-Pentagon Angle:  acos(sqrt(15*(5−2*sqrt(5)))/15)    ≈79.187683036 degrees
Hexagon-Triangle Angle:  acos(sqrt(5)/3)    ≈318.189685104 degrees
Dual Solid:  Great Icosacronic Hexecontahedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(2*(17−3*sqrt(5)))/4    ≈1.1342285961998925302
Midscribed Radius:  sqrt(6*(5−sqrt(5)))/4    ≈1.0180739209102543669
Hexagon Center Radius:  (sqrt(15)−sqrt(3))/4    ≈0.53523313465963489791
Pentagon Center Radius:  sqrt(10*(65−19*sqrt(5)))/20    ≈0.750245100408926292247
Triangle Center Radius:  (9*sqrt(3)−sqrt(15))/12    ≈0.976289493492706563047


References:[1]Jean Paul Albert Badoureau, Mémoire sur les Figures Isocèles,
Journal de l'École polytechnique 49 (1881), 47-172.