Self-Intersecting Quasi-Quasi-Regular Polyhedra

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)

(Uniform #33) Small Dodecicosidodecahedron
Vertices:  60  (60[4])
Faces:44  (20 equilateral triangles + 12 regular pentagons
    + 12 regular decagons)
Edges:120
Symmetry:  Full Icosahedral  (Ih)
Decagon-Pentagon Angle:  acos(−sqrt(5)/5)    ≈116.565051177 degrees
Decagon-Triangle Angle:  acos(sqrt(15*(5+2*sqrt(5)))/15)    ≈322.622631859 degrees
Dual Solid:  Small Dodecacronic Hexecontahedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(11+4*sqrt(5))/2    ≈2.2329505094156900495004
Midscribed Radius:  sqrt(2*(5+2*sqrt(5)))/2    ≈2.1762508994828215111
Decagon Center Radius:  sqrt(5+2*sqrt(5))/2    ≈1.5388417685876267013
Pentagon Center Radius:  3*sqrt(5*(5+2*sqrt(5)))/10    ≈2.0645728807067603073
Triangle Center Radius:  (3*sqrt(3)+2*sqrt(15))/6    ≈2.1570198525202442752


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