# Cellirhombated tesseractic tetracomb

Cellirhombated tesseractic tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymCartit
Coxeter diagramx4o3x3o4x ()
Elements
Tera3N tesseracts, 4N small rhombicuboctahedral prisms, N small rhombated tesseracts
Cells32N triangular prisms, 8N octahedra, 24N+24N cubes, 8N small rhombicuboctahedra
Faces64N triangles, 24N+48N+96N squares
Edges96N+96N
Vertices48N
Vertex figureAntiduowedge, edge lengths 1 (edges of top square) and 2 (remaining edges)
Related polytopes
ArmyCartit
RegimentCartit
ConjugateQuasicelliquasirhombated tesseractic tetracomb
Abstract & topological properties
OrientableYes
Properties
SymmetryR5×2
ConvexYes
NatureTame

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:

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

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