Geodesic Icosahedra

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Geodesic Icosahedron Pattern 4 [3,0]
(Hexakis-Pentakis Truncated Icosahedron)
Vertices:  92  (12[5] + 20[6] + 60[6])
Faces:180  ({120 + 60} isosceles triangles)
Edges:270  (60 short + 90 medium + 120 long)
Symmetry:  Full Icosahedral  (Ih)
Dual Solid:  Dual Geodesic Icosahedron Pattern 4 [3,0]
(values below based on edge-scribed radius = 1)
Short Edge (60):  (149*sqrt(5)−77)/723    ≈0.35432106313619455707
Medium Edge (90):  (sqrt(5)−1)/3    ≈0.41202265916659656547
Long Edge (120):  2*(14*sqrt(5)−32−9*sqrt(3)    
    +6*sqrt(15))/33    
≈0.42147845418919160115497
Edge-scribed Radius:  1
Volume:20*(55547+49164*sqrt(3)−20051*sqrt(5)    
    −22172*sqrt(15))/47718    
≈4.1889266668163598131