Self-Intersecting Truncated Quasi-Regular Polyhedra

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(Uniform #68) Great Truncated Icosidodecahedron
Vertices:  120  (120[3])
Faces:62  (30 squares + 20 regular hexagons + 12 regular decagrams)
Edges:180
Symmetry:  Full Icosahedral  (Ih)
Hexagon-Square Angle:  acos((sqrt(15)−sqrt(3))/6)    ≈69.094842552 degrees
Decagram-Hexagon Angle:  acos(sqrt(15*(5−2*sqrt(5)))/15)    ≈79.187683036 degrees
Decagram-Square Angle:  acos(−sqrt(10*(5−sqrt(5)))/10)    ≈121.717474411 degrees
Dual Solid:  Great Disdyakis Triacontahedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(31−12*sqrt(5))/2    ≈1.0206841173941284126
Midscribed Radius:  sqrt(6*(5−2*sqrt(5)))/2    ≈0.88982923502244570318
Hexagon Center Radius:  (sqrt(15)−2*sqrt(3))/2    ≈0.20444086553483114906
Square Center Radius:  (2*sqrt(5)−3)/2    ≈0.73606797749978969641
Decagram Center Radius:  sqrt(5*(5−2*sqrt(5)))/2    ≈0.81229924058226581539


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.