Icosafold icosidodecaswirlchoron

Icosafold icosidodecaswirlchoron
File:Icosafold icosidodecaswirlchoron.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	1200 phyllic disphenoids, 240 pentagonal gyroprisms
Faces	2400 scalene triangles, 1200 isosceles triangles, 240 pentagons
Edges	600+1200+1200
Vertices	600
Vertex figure	Polyhedron with 4 tetragons and 8 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Rhombitriacontaswirlic hexacosichoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H3●I2(20), order 2400
Convex	Yes
Nature	Tame

The icosafold icosidodecaswirlchoron is an isogonal polychoron with 240 pentagonal gyroprisms, 1200 phyllic disphenoids, and 600 vertices. 4 pentagonal gyroprisms and 8 phyllic disphenoids join at each vertex. It is the fifth in an infinite family of isogonal icosidodecahedral swirlchora.

The ratio between the longest and shortest edges is 1:${\frac {\sqrt {7-{\sqrt {5}}+2{\sqrt {5-2{\sqrt {5}}}}}}{2}}$ ≈ 1:1.24670.