# Truncated tesseractic tetracomb

Truncated tesseractic tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymTattit
Coxeter diagramx4x3o3o4o ()
Elements
Cells16N tetrahedra, 4N truncated cubes
Faces32N triangles, 6N octagons
Edges4N+24N
Vertices8N
Vertex figureOctahedral pyramid, edge lengths 1 (base) and 2+2 (sides)
Related polytopes
ArmyTattit
RegimentTattit
ConjugateQuasitruncated tesseractic tetracomb
Abstract & topological properties
OrientableYes
Properties
SymmetryR5
ConvexYes
NatureTame

The truncated tesseractic tetracomb, or tattit, is a convex uniform tetracomb. 1 hexadecachoron and 8 truncated tesseracts join at each vertex of this tessellation. As the name suggests, it is the truncation of the tesseractic tetracomb.

## Vertex coordinates

The vertices of a truncated cubic honeycomb of edge length 1 are given by all permutations of:

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

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

## Representations

A truncated tesseractic tetracomb has the following Coxeter diagrams:

• x4x3o3o4o () (full symmetry)
• o3o3x4x *b3o () (half symmetry)