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)