Retroantiprismatosnub dishecatonicosachoron

Retroantiprismatosnub dishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
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	${\frac {1+{\sqrt {5}}}{2}}\approx 1.61803$
Hypervolume	${\frac {135{\sqrt {5}}+325}{2}}\approx 313.43459$
Central density	–16
Related polytopes
Army	Non-uniform Thi
Regiment	Rapsady
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	288000
Euler characteristic	–1200
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 has ditrigonary dodecadodecahedra as pseudocells.

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".