Kepler-Poinsot Solids

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(Uniform #35) Great Dodecahedron
Vertices:  12  (12[5])
Faces:12  (regular pentagons)
Edges:30
Symmetry:  Full Icosahedral  (Ih)
Dihedral Angle:  acos(sqrt(5)/5)    ≈63.434948823 degrees
Dual Solid:  Small Stellated Dodecahedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(2*(5+sqrt(5)))/4    ≈0.95105651629515357212
Midscribed Radius:  (1+sqrt(5))/4    ≈0.80901699437494742410
Inscribed Radius:  sqrt(10*(5+sqrt(5)))/20    ≈0.42532540417601996609


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