Self-Intersecting Snub Quasi-Regular Polyhedra
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(Uniform #75)
Great Dirhombicosidodecahedron
Vertices:
60 (60[8])
Faces:
124 (40 equilateral triangles + 60 squares + 24 regular pentagrams)
Edges:
240
Symmetry:
Full Icosahedral (Ih)
Square-Triangle Angle:
acos(sqrt(3)/3)
≈54.735610317 degrees
Pentagram-Square Angle:
acos(sqrt(5*(5−2*sqrt(5)))/5)
≈71.039290118 degrees
Dual Solid:
Great Dirhombicosidodecacron
(values below based on edge length = 1)
Circumscribed Radius:
sqrt(2)/2
≈0.70710678118654752440
Midscribed Radius:
1/2
0.5
Square Center Radius:
0
Triangle Center Radius:
sqrt(6)/6
≈0.40824829046386301637
Pentagram Center Radius:
sqrt(10*sqrt(5))/10
≈0.472870804501587906651
References:
[1]
H. S. M. Coxeter, M. S. Longuet-Higgins, and J. C. P. Miller,
Uniform Polyhedra,
Philosophical Transactions of the Royal Society of London.
Series A. Mathematical and Physical Sciences
246
(1954), 401-450.