Versi-Quasi-Regular Polyhedra

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(Uniform #73) Great Rhombidodecahedron
Vertices:  60  (60[4])
Faces:42  (30 squares + 12 regular decagrams)
Edges:120
Symmetry:  Full Icosahedral  (Ih)
Dihedral Angle 1 (60):  acos(sqrt(10*(5+sqrt(5)))/10)    ≈31.717474411 degrees
Dihedral Angle 2 (60):  acos(sqrt(10*(5−sqrt(5)))/10)    ≈58.282525589 degrees
Dual Solid:  Great Rhombidodecacron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(11−4*sqrt(5))/2    ≈0.71689052337174209824
Midscribed Radius:  sqrt(2*(5−2*sqrt(5)))/2    ≈0.51374314837300779674
Square Center Radius:  (sqrt(5)−2)/2    ≈0.11803398874989484820
Decagram Center Radius:  sqrt(5−2*sqrt(5))/2    ≈0.363271264002680442948


References:[1]Jean Paul Albert Badoureau, Mémoire sur les Figures Isocèles,
Journal de l'École polytechnique 49 (1881), 47-172.