Retroantiprismatosnub dishecatonicosachoron

Retroantiprismatosnub dishecatonicosachoron
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Rapsady
Elements
Cells	1440 pentagonal antiprisms, 120 small snub icosicosidodecahedra, 120 small inverted retrosnub icosicosidodecahedra
Faces	1440 pentagons, 1440 pentagrams, 7200+7200 triangles, 2400 irregular hexagrams
Edges	7200+14400
Vertices	2400
Measures (edge length 1)
Circumradius	$\frac{1+\sqrt5}{2} ≈ 1.61803$
Hypervolume	$\frac{135\sqrt5+325}{2} ≈ 313.43459$
Central density	–16
Related polytopes
Army	Non-uniform Thi
Regiment	Rapsady
Convex core	Hecatonicosachoron
Abstract properties
Euler characteristic	–1200
Topological properties
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The retroantiprismatosnub dishecatonicosachoron, or rapsady, is a nonconvex uniform polychoron that consists of 1440 pentagonal antiprisms, 120 small snub icosicosidodecahedra, and 120 small inverted retrosnub icosicosidodecahedra. 6 pentagonal antiprisms, 3 small snub icosicosidodecahedra, and 3 small inverted retrosnub icosicosidodecahedra join at each vertex.

It is the only currently known non-prismatic uniform polychoron to contain snub cells with dodecahedral symmetry.

Cross-sections

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External links

• Bowers, Jonathan. "Category 20: Miscellaneous" (#974).

• Klitzing, Richard. "rapsady".