Celligreatorhombated tesseractic tetracomb

Celligreatorhombated tesseractic tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Cagratit
Coxeter diagram	x4x3x3o4x ()
Elements
Tera	6N square-octagonal duoprisms, 4N small rhombicuboctahedral prisms, 4N great rhombicuboctahedral prisms, N great rhombated tesseracts, N prismatorhombated tesseracts
Cells	32N triangular prisms, 24N+24N+48N cubes, 32N hexagonal prisms, 16N truncated tetrahedra, 24N octagonal prisms, 8N small rhombicuboctahedra, 8N great rhombicuboctahedra
Faces	64N triangles, 48N+96N+96N+96N+96N squares, 64N hexagons, 24N octagons
Edges	96N+96N+192N+192N
Vertices	192N
Vertex figure	Isosceles trapezoidal pyramidal pyramid, base edge lengths 1, √2, √2, √2, remaining edge lengths √2 (6), √3 (2), and √2+√2 (1)
Related polytopes
Army	Cagratit
Regiment	Cagratit
Conjugate	Quasicelligreatoquasirhombated tesseractic tetracomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5
Convex	Yes

The celligreatorhombated tesseractic tetracomb or cagratit, also called the stericantitruncated tesseractic tetracomb, is a convex uniform tetracomb. 1 great rhombated tesseract, 1 prismatorhombated tesseract, 1 small rhombicuboctahedral prism, 2 great rhombicuboctahedral prisms, and 1 square-octagonal duoprism join at each vertex of this tessellation. As the name suggests, it is the stericantitruncation of the tesseractic tetracomb.

Vertex coordinates

The vertices of a celligreatorhombated tesseractic tetracomb of edge length 1 are given by all permutations of:

• $\left(±\frac12+(2+2\sqrt2)i,\,±\frac{1+\sqrt2}{2}+(2+2\sqrt2)j,\,±\frac{1+2\sqrt2}{2}+(2+2\sqrt2)k,\,±\frac{1+2\sqrt2}{2}+(2+2\sqrt2)l\right),$

Where i, j, k, and l range over the integers.

External links

• Klitzing, Richard. "cagratit".

• Wikipedia Contributors. "Stericantitruncated tesseractic honeycomb".