Self-Intersecting Quasi-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 #43) Small Ditrigonal Dodecicosidodecahedron
Vertices:  60  (60[4])
Faces:44  (20 equilateral triangles + 12 regular pentagrams
    + 12 regular decagons)
Edges:120
Symmetry:  Full Icosahedral  (Ih)
Decagon-Triangle Angle:  acos(−sqrt(15*(5−2*sqrt(5)))/15)    ≈100.812316964 degrees
Decagon-Pentagram Angle:  acos(sqrt(5)/5)    ≈296.565051177 degrees
Dual Solid:  Small Ditrigonal Dodecacronic Hexecontahedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(2*(17+3*sqrt(5)))/4    ≈1.7214893236852853443
Midscribed Radius:  sqrt(6*(5+sqrt(5)))/4    ≈1.6472782070926638518
Decagon Center Radius:  sqrt(2*(5−sqrt(5)))/4    ≈0.58778525229247312917
Triangle Center Radius:  (9*sqrt(3)+sqrt(15))/12    ≈1.6217867178606093772
Pentagram Center Radius:  sqrt(10*(65+19*sqrt(5)))/20    ≈1.6392474765307403412


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.