Self-Intersecting Snub Quasi-Regular Polyhedra

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(Uniform #57) Great Snub Icosidodecahedron
Vertices:  60  (60[5])
Faces:92  (80 equilateral triangles + 12 regular pentagrams)
Edges:150
Symmetry:  Chiral Icosahedral  (I)
Triangle-Triangle Angle:  acos(-root[729*(x^6)+486*(x^5)−729*(x^4)    
    −756*(x^3)+63*(x^2)+270*x+1])    
≈126.823151217 degrees
Pentagram-Triangle Angle:  acos(−sqrt(root[91125*(x^6)−668250*(x^5)    
    +2006775*(x^4)−2735100*(x^3)    
    +1768275*(x^2)−502410*x+43681]))    
≈138.822370251 degrees
Dual Solid:  Great Pentagonal Hexecontahedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(root[4096*(x^6)−27648*(x^5)    
    +47104*(x^4)−35776*(x^3)    
    +13872*(x^2)−2696*x+209])    
≈0.81608067479992340018
Midscribed Radius:  sqrt(root[4096*(x^6)−21504*(x^5)    
    +16384*(x^4)−4672*(x^3)    
    +624*(x^2)−40*x+1])    
≈0.64497105964678626948
Triangle Center Radius:  sqrt(root[2985984*(x^6)−14183424*(x^5)    
    +5723136*(x^4)−478656*(x^3)    
    +12528*(x^2)−360*x+1])    
≈0.57676193914696295469
Pentagram Center Radius:  sqrt(root[512000*(x^6)−1920000*(x^5)    
    −460800*(x^4)+424000*(x^3)    
    +53040*(x^2)−20600*x+961])    
≈0.62417502796241159892


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.
[2]J. Lesavre and R. Mercier, Dix Nouveaux Polyèdres Semi-régulièrs sans Plan
de Symétrie, Comptes Rendus des Séances de l'Académie des Sciences 224
(1947), 785-786.