Self-Intersecting Quasi-Regular Polyhedra

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(Uniform #30) Small Ditrigonal Icosidodecahedron
Vertices:  20  (20[6])
Faces:32  (20 equilateral triangles + 12 regular pentagrams)
Edges:60
Symmetry:  Full Icosahedral  (Ih)
Dihedral Angle:  acos(−sqrt(15*(5+2*sqrt(5)))/15)    ≈142.622631859 degrees
Dual Solid:  Small Triambic Icosahedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(3)/2    ≈0.86602540378443864676
Midscribed Radius:  sqrt(2)/2    ≈0.70710678118654752440
Triangle Center Radius:  sqrt(15)/6    ≈0.64549722436790281420
Pentagram Center Radius:  sqrt(5*(5+2*sqrt(5)))/10    ≈0.68819096023558676910


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.