Self-Intersecting Snub Quasi-Regular Polyhedra

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)
Please use a browser that supports "canvas"

(Uniform #75) Great Dirhombicosidodecahedron
Vertices:  60  (60[8])
Faces:124  (40 equilateral triangles + 60 squares + 24 regular pentagrams)
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.