Self-Intersecting Snub Quasi-Regular Polyhedra

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(Uniform #60) Inverted Snub Dodecadodecahedron
Vertices:  60  (60[5])
Faces:84  (60 equilateral triangles + 12 regular pentagons
    + 12 regular pentagrams)
Edges:150
Symmetry:  Chiral Icosahedral  (I)
Pentagon-Triangle Angle:  acos(sqrt(root[4100625*(x^8)−32805000*(x^7)    
    +95863500*(x^6)−119799000*(x^5)    
    +68311350*(x^4)−20763000*(x^3)    
    +7189740*(x^2)−2234280*x+201601]))    
≈68.640878254 degrees
Triangle-Triangle Angle:  acos(−sqrt(root[6561*(x^4)−20412*(x^3)    
    +30942*(x^2)−20556*x+4489]))    
≈130.490738467 degrees
Pentagram-Triangle Angle:  acos(sqrt(root[4100625*(x^8)−32805000*(x^7)    
    +95863500*(x^6)−119799000*(x^5)    
    +68311350*(x^4)−20763000*(x^3)    
    +7189740*(x^2)−2234280*x+201601]))    
≈11.124480107 degrees
Dual Solid:  Medial Inverted Pentagonal Hexecontahedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(root[64*(x^4)−192*(x^3)    
    +180*(x^2)−65*x+8])    
≈0.851630228117412395153
Midscribed Radius:  sqrt(root[256*(x^4)−512*(x^3)    
    +240*(x^2)−28*x+1])    
≈0.68940122239760778779
Pentagon Center Radius:  sqrt(root[2560000*(x^8)−5120000*(x^7)    
    +1088000*(x^6)+1968000*(x^5)    
    −407600*(x^4)−195400*(x^3)    
    +21445*(x^2)−635*x+1])    
≈0.040831944520643442918
Triangle Center Radius:  sqrt(root[5184*(x^4)−8640*(x^3)    
    +2484*(x^2)+39*x+1])    
≈0.62605168485515837671
Pentagram Center Radius:  −sqrt(root[2560000*(x^8)−5120000*(x^7)    
    +1088000*(x^6)+1968000*(x^5)    
    −407600*(x^4)−195400*(x^3)    
    +21445*(x^2)−635*x+1])    
≈−0.66998570372306814123


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.