Archimedean-Catalan Hulls

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Joined Icosidodecahedron
Vertices:  62  (20[3] + 30[4] + 12[5])
Faces:60  (kites)
Edges:120  (60 short + 60 long)
Symmetry:  Full Icosahedral  (Ih)
Long Edge Angle:  acos(−(15+sqrt(5))/20)    ≈149.5196754346 degrees
Short Edge Angle:  acos(−(5+2*sqrt(5))/10)    ≈161.3005929149 degrees
(values below based on unit-edge-length Icosidodecahedron)
Short Edge (60):  sqrt(2*(13−sqrt(5)))/8    ≈0.57997661651408979196
Long Edge (60):  sqrt(9+2*sqrt(5))/4    ≈0.91761020983175296841
Kite Length:  sqrt(10*(5+sqrt(5)))/8    ≈1.0633135104400499152
Kite Width:  1
[3]-Vertex Radius (20):  (5*sqrt(3)+sqrt(15))/8    ≈1.5666546730064754191
[4]-Vertex Radius (30):  (1+sqrt(5))/2    ≈1.6180339887498948482
[5]-Vertex Radius (12):  sqrt(5*(5+2*sqrt(5)))/4    ≈1.7204774005889669228
Inscribed Radius:  sqrt(5+2*sqrt(5))/2    ≈1.5388417685876267013
Volume:25*(3+sqrt(5))/8    ≈16.362712429686842801


References:[1]Conway Notation for Polyhedra (George Hart)