Skewverted tetrishecatonicosachoron

Skewverted tetrishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Kevuthi
Coxeter diagram	x5x5o5/3x5/3*a3/2*c *b3*d
Elements
Cells	120 small dodecicosidodecahedra, 120 icosidodecadodecahedra, 120 great dodecicosidodecahedra, 120 icosidodecatruncated icosidodecahedra
Faces	2400 triangles, 1440 pentagons, 1440 pentagrams, 2400 hexagons, 1440 decagons, 1440 decagrams
Edges	7200+7200+7200
Vertices	7200
Vertex figure	Crossed skewed wedge, base edge lengths 1, (√5–1)/2, (1+√5)/2; lateral edge lengths √3, √(5+√5)/2, √(5–√5)/2
Measures (edge length 1)
Circumradius	$2{\sqrt {2}}\approx 2.82843$
Hypervolume	3800
Dichoral angles	Gaddid–5/2–ided: 144°
	Gaddid–10/3–idtid: 144°
	Saddid–10–idtid: 144°
	Gaddid–3–saddid: 120°
	Saddid–5–ided: 108°
	Ided–6–idtid: 60°
Related polytopes
Army	Semi-uniform Prix
Regiment	Sik vipathi
Conjugate	Skewverted tetrishecatonicosachoron
Abstract & topological properties
Euler characteristic	–4320
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The skewverted tetrishecatonicosachoron, or kevuthi, is a nonconvex uniform polychoron that consists of 120 small dodecicosidodecahedra, 120 icosidodecadodecahedra, 120 great dodecicosidodecahedra, and 120 icosidodecatruncated icosidodecahedra. 1 small dodecicosidodecahedron, 1 icosidodecadodecahedron, 1 great dodecicosidodecahedron, and 2 icosidodecatruncated icosidodecahedra join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small skewverted prismatotrishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 14: Skewverts" (#583).