Self-Intersecting Quasi-Quasi-Regular Polyhedra

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(Uniform #38) Rhombidodecadodecahedron
Vertices:  60  (60[4])
Faces:54  (30 squares + 12 regular pentagons
    + 12 regular pentagrams)
Edges:120
Symmetry:  Full Icosahedral  (Ih)
Pentagon-Square Angle:  acos(−sqrt(10*(5−sqrt(5)))/10)    ≈121.717474411 degrees
Pentagram-Square Angle:  acos(−sqrt(10*(5+sqrt(5)))/10)    ≈148.282525589 degrees
Dual Solid:  Medial Deltoidal Hexecontahedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(7)/2    ≈1.3228756555322952953
Midscribed Radius:  sqrt(6)/2    ≈1.2247448713915890491
Pentagon Center Radius:  sqrt(5*(25−2*sqrt(5)))/10    ≈1.0131106564684930953
Square Center Radius:  sqrt(5)/2    ≈1.1180339887498948482
Pentagram Center Radius:  sqrt(5*(25+2*sqrt(5)))/10    ≈1.2139220723547203751


References:[1]Jean Paul Albert Badoureau, Mémoire sur les Figures Isocèles,
Journal de l'École polytechnique 49 (1881), 47-172.
[2]Johann Pitsch, Über Halbreguläre Sternpolyeder,
Zeitschrift für das Realschulwesen 6 (1881), 9-24, 64-65, 72-89, 216.