Kepler-Poinsot Solids

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(Uniform #34) Small Stellated Dodecahedron
Vertices:  12  (12[5])
Faces:12  (regular pentagrams)
Symmetry:  Full Icosahedral  (Ih)
Dihedral Angle:  acos(−sqrt(5)/5)    ≈116.565051177 degrees
Dual Solid:  Great 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:  sqrt(10*(5−sqrt(5)))/20    ≈0.26286555605956680301

References:[1]Johannes Kepler, Harmonices Mundi (1619).
[2]Johannes Kepler with E. J. Aiton, A. M. Duncan,
and J. V. Field, translators, The Harmony of the World,
American Philosophical Society (1997).