Kepler-Poinsot Solids

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(Uniform #52) Great Stellated Dodecahedron
Vertices:  20  (20[3])
Faces:12  (regular pentagrams)
Symmetry:  Full Icosahedral  (Ih)
Dihedral Angle:  acos(sqrt(5)/5)    ≈63.434948823 degrees
Dual Solid:  Great Icosahedron
(values below based on edge length = 1)
Circumscribed Radius:  (sqrt(15)−sqrt(3))/4    ≈0.53523313465963489791
Midscribed Radius:  (3−sqrt(5))/4    ≈0.19098300562505257590
Inscribed Radius:  sqrt(10*(25−11*sqrt(5)))/20    ≈0.10040570794311363993

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).