Celligreatorhombated icosiheptaheptacontadipeton

Celligreatorhombated icosiheptaheptacontadipeton
Rank	6
Type	Uniform
Notation
Bowers style acronym	Cograjik
Coxeter diagram	x3x3x3o3x *c3o ()
Elements
Peta	27 great rhombated triacontaditera 27 prismatotruncatodemipenteracts 72 celligreatorhombated hexatera 216 small rhombated pentachoric prisms 216 great rhombated pentachoric prisms
Tera	2160 triangular-square duoprisms 720 triangular-hexagonal duoprisms 1080 octahedral prisms 1080 cuboctahedral prisms 1080 truncated tetrahedral prisms 1080 truncated octahedral prisms 432 small rhombated pentachora 864 great rhombated pentachora 432 prismatorhombated pentachora 270 truncated hexadecachora
Vertices	12960
Vertex figure	Irregular triangular-prismatic scalene
Measures (edge length 1)
Circumradius	${\sqrt {\frac {53}{3}}}\approx 4.20317$
Hypervolume	${\frac {1573843{\sqrt {3}}}{160}}\approx 17037.35024$
Central density	1
Number of external pieces	558
Related polytopes
Army	Cograjik
Regiment	Cograjik
Conjugate	None
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	E6, order 51840
Convex	Yes
Nature	Tame

The celligreatorhombated icosiheptaheptacontadipeton or cograjik, also called the stericantitruncated 2₂₁ polytope, is a convex uniform polypeton. It consists of 27 great rhombated triacontaditera, 27 prismatotruncated demipenteracts, 72 celligreatorhombated hexatera, 216 small rhombated pentachoric prisms, and 216 great rhombated pentachoric prisms. 1 great rhombated triacontaditeron, 1 prismatotruncated demipenteract, 2 celligreatorhombated hexatera, 1 small rhombated pentachoric prism, and 2 great rhombated pentachoric prisms join at each vertex.