Cellirhombated tesseractic tetracomb

Cellirhombated tesseractic tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Cartit
Coxeter diagram	x4o3x3o4x ()
Elements
Tera	3N tesseracts, 4N small rhombicuboctahedral prisms, N small rhombated tesseracts
Cells	32N triangular prisms, 8N octahedra, 24N+24N cubes, 8N small rhombicuboctahedra
Faces	64N triangles, 24N+48N+96N squares
Edges	96N+96N
Vertices	48N
Vertex figure	Antiduowedge, edge lengths 1 (edges of top square) and √2 (remaining edges)
Related polytopes
Army	Cartit
Regiment	Cartit
Conjugate	Quasicelliquasirhombated tesseractic tetracomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5×2
Convex	Yes
Nature	Tame

The cellirhombated tesseractic tetracomb or cartit, also called the stericantellated tesseractic tetracomb is a convex uniform tetracomb. 2 small rhombated tesseracts, 4 small rhombicuboctahedral prisms, and 1 tesseract join at each vertex of this tessellation. As the name suggests, it is the stericantellation of the tesseractic tetracomb.

Vertex coordinates

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

• $\left(\pm {\frac {1}{2}}+(2+{\sqrt {2}})i,\,\pm {\frac {1}{2}}+(2+{\sqrt {2}})j,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(2+{\sqrt {2}})k,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(2+{\sqrt {2}})l\right)$,

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

External links

• Klitzing, Richard. "cartit".
• Wikipedia contributors. "Stericantellated tesseractic honeycomb".