Catalan Solids

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Pentagonal Hexecontahedron (dextro)
canonical form
Vertices:  92  (80[3] + 12[5])
Faces:60  (mirror-symmetric pentagons)
Edges:150  (90 short + 60 long)
Symmetry:  Chiral Icosahedral  (I)
Dihedral Angle:  acos(−(2*(x+(2/x))*(15*phi+1)    
    +(16*phi+15))/209)    
≈153.178732558 degrees
where:  phi = (1+sqrt(5))/2
x = cbrt((phi+sqrt(phi−5/27))/2)+cbrt((phi−sqrt(phi−5/27))/2)
Dual Solid:  Snub Dodecahedron (laevo)
(values below based on unit-edge-length Snub Dodecahedron)
Short Edge (90):  1/x≈0.58289953474498241442
Long Edge (60):  (x*(7*phi+2)+(5*phi-3)+2*(8-3*phi)/x)/31    ≈1.0199882470228458983
[3]-Vertex Radius (80):  sqrt(3*(x*phi+phi+1+(1/x)))/2    ≈2.1172098986276657420
[5]-Vertex Radius (12):  sqrt((x^2)*(1067*phi+1009)    
    +x*(2259*phi+1168)+(941*phi+1097))/62    
≈2.2200006991613182111
Edge-scribed Radius:  phi*sqrt(x*(x+phi)+1)/2    ≈2.0970538352520879924
Inscribed Radius:  x*sqrt(209*((x^2)*(104*phi-7)    
    +x*(153*phi+52)+(195-phi)))/418    
≈2.0398731549542789999
Volume:5*sqrt(x*((x^2)*(11405*phi+287)    
    +x*(14528*phi+8265)+(2363*phi+13146)))/62    
≈37.588423673993486442


References:[1]Eugène Catalan, Mémoire sur la Théorie des Polyèdres,
Journal de l'École polytechnique 41 (1865), 1-71, +7 plates.