Self-Intersecting Snub Quasi-Regular Polyhedra

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(Uniform #46) Snub Icosidodecadodecahedron
Vertices:  60  (60[6])
Faces:104  (80 equilateral triangles + 12 regular pentagons
    + 12 regular pentagrams)
Edges:180
Symmetry:  Chiral Icosahedral  (I)
Pentagram-Triangle Angle:  acos(sqrt(root[91125*(x^6)−425250*(x^5)    
    +888975*(x^4)−607500*(x^3)    
    +53955*(x^2)−690*x+3481]))    
≈7.352138644 degrees
Pentagon-Triangle Angle:  acos(−sqrt(root[91125*(x^6)−425250*(x^5)    
    +888975*(x^4)−607500*(x^3)    
    +53955*(x^2)−690*x+3481]))    
≈120.434012966 degrees
Triangle-Triangle Angle:  acos(−(1+cbrt(4*(25+3*sqrt(69)))    
    +cbrt(4*(25−3*sqrt(69))))/9)    
≈146.781253328 degrees
Dual Solid:  Medial Hexagonal Hexecontahedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(6*(16+cbrt(4*(97+3*sqrt(69)))    
    +cbrt(4*(97−3*sqrt(69)))))/12    
≈1.12689791279993934351
Midscribed Radius:  sqrt(6*(10+cbrt(4*(97+3*sqrt(69)))    
    +cbrt(4*(97−3*sqrt(69)))))/12    
≈1.0099004435452336687
Pentagon Center Radius:  sqrt(root[512000*(x^6)−512000*(x^5)    
    −140800*(x^4)+131200*(x^3)    
    +17040*(x^2)−5480*x+361])    
≈0.73911576097583031237
Triangle Center Radius:  sqrt(6*(8+cbrt(4*(97+3*sqrt(69)))    
    +cbrt(4*(97−3*sqrt(69)))))/12    
≈0.96776317998750415529
Pentagram Center Radius:  −sqrt(root[512000*(x^6)−512000*(x^5)    
    −140800*(x^4)+131200*(x^3)    
    +17040*(x^2)−5480*x+361])    
≈−0.99674756263701927657


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.