Small rhombated tesseractic tetracomb

Small rhombated tesseractic tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Srittit
Coxeter diagram	x4o3x3o4o ()
Elements
Tera	4N octahedral prisms, N icositetrachora, N small rhombated tesseracts
Cells	32N triangular prisms, 8N+16N octahedra, 4N small rhombicuboctahedra
Faces	32N+64N triangles, 6N+48N squares
Edges	24N+96N
Vertices	24N
Vertex figure	Square pyramidal prism, edge lengths 1 (base cube) and √2 (sides and top edge)
Related polytopes
Army	Srittit
Regiment	Srittit
Conjugate	Quasirhombated tesseractic tetracomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5
Convex	Yes

The small rhombated tesseractic tetracomb or srittit, also called the cantellated tesseractic tetracomb is a convex uniform tetracomb. 4 small rhombated tesseracts, 2 icositetrachora, and 1 octahedral prism join at each vertex of this tessellation. As the name suggests, it is the cantellation of the tesseractic tetracomb.

Vertex coordinates

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

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

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

Representations

A small rhombated tesseractic tetracomb has the following Coxeter diagrams:

• x4o3x3o4o (full symmetry)
• o3x3o *b3o4x (half symmetry)

External links

• Klitzing, Richard. "srittit".

• Wikipedia Contributors. "Cantellated tesseractic honeycomb".