# Rectified tesseractic tetracomb

Rectified tesseractic tetracomb
Rank5
TypeQuasiregular
SpaceEuclidean
Notation
Bowers style acronymRittit
Coxeter diagramo4x3o3o4o ()
Elements
Cells16N tetrahedra, 4N cuboctahedra
Faces32N triangles, 6N squares
Edges24N
Vertices4N
Vertex figureOctahedral prism, edge lengths 1 (base) and 2 (sides
Related polytopes
ArmyRittit
RegimentRittit
DualJoined tesseractic tetracomb
ConjugateNone
Abstract & topological properties
OrientableYes
Properties
SymmetryR5
ConvexYes
NatureTame

The rectified tesseractic tetracomb, or rittit, is a convex uniform tetracomb. 2 hexadecachora and 8 rectified tesseracts join at each vertex of this tessellation. As the name suggests, it is the rectification of the tesseractic tetracomb.

## Vertex coordinates

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

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

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

## Representations

A rectified tesseractic tetracomb has the following Coxeter diagrams:

• o4x3o3o4o () (full symmetry)
• o3o3x4o *b3o () (half symmetry, tetratetrahedral prism verf)
• x3o3o4o *b3x () (half symmetry, octahedral frustum verf)
• x3o3x *b3o *b3o () (quarter symmetry, tetratetrahedral frustum verf)