# Rectified icositetrachoric tetracomb

Jump to navigation Jump to search
Rectified icositetrachoric tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymRicot
Coxeter diagramo3x4o3o3o ()
Elements
Tera3N tesseracts, N rectified icositetrachora
Cells24N cubes, 12N cuboctahedra
Faces32N triangles, 72N squares
Edges96N
Vertices24N
Vertex figureTetrahedral prism, edge lengths 2 (base) and 1 (side)
Related polytopes
ArmyRicot
RegimentRicot
ConjugateNone
Abstract & topological properties
OrientableYes
Properties
SymmetryU5
ConvexYes
NatureTame

The rectified icositetrachoric tetracomb, or ricot, is a convex uniform tetracomb. 4 rectified icositetrachora and 2 tesseracts join at each vertex of this tessellation. As the name suggests, it is the rectification of the icositetrachoric tetracomb.

## Vertex coordinates

The vertices of a rectified icositetrachoric tetracomb of edge length 1 are given by all permutations of:

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

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

## Representations

A rectified icositetrachoric tetracomb has the following Coxeter diagrams: