Kepler-Poinsot Solids

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(Uniform #53) Great Icosahedron
Vertices:  12  (12[5])
Faces:20  (equilateral triangles)
Edges:30
Symmetry:  Full Icosahedral  (Ih)
Dihedral Angle:  acos(sqrt(5)/3)    ≈41.810314896 degrees
Dual Solid:  Great Stellated Dodecahedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(2*(5−sqrt(5)))/4    ≈0.58778525229247312917
Midscribed Radius:  (sqrt(5)−1)/4    ≈0.30901699437494742410
Inscribed Radius:  (3*sqrt(3)−sqrt(15))/12    ≈0.11026408970826791628


References:[1]Louis Poinsot, Mémoire sur les Polygones et Polyèdres,
Journal de l'École polytechnique 10 (1810), 16-48.