Self-Intersecting Quasi-Regular Polyhedra

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(Uniform #36) Dodecadodecahedron
Vertices:  30  (30[4])
Faces:24  (12 regular pentagons + 12 regular pentagrams)
Edges:60
Symmetry:  Full Icosahedral  (Ih)
Dihedral Angle:  acos(−sqrt(5)/5)    ≈116.565051177 degrees
Dual Solid:  Medial Rhombic Triacontahedron
(values below based on edge length = 1)
Circumscribed Radius:  1
Midscribed Radius:  sqrt(3)/2    ≈0.86602540378443864676
Pentagon Center Radius:  sqrt(10*(5−sqrt(5)))/10    ≈0.52573111211913360603
Pentagram Center Radius:  sqrt(10*(5+sqrt(5)))/10    ≈0.85065080835203993218


References:[1]Edmund Hess, Über vier Archimedeische Polyeder höherer Art,
Schriften der Gesellschaft zur Beförderung der gesammten
Naturwissenschaften zu Marburg 11(4) (1878).
[2]Jean Paul Albert Badoureau, Mémoire sur les Figures Isocèles,
Journal de l'École polytechnique 49 (1881), 47-172.
[3]Johann Pitsch, Über Halbreguläre Sternpolyeder, Zeitschrift
für das Realschulwesen 6 (1881), 9-24, 64-65, 72-89, 216.