# Bitruncated tesseractic tetracomb

Bitruncated tesseractic tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymBatitit
Coxeter diagramo4x3x3o4o ()
Elements
Cells4N octahedra, 16N truncated tetrahedra, 4N truncated octahedra
Faces32N triangles, 6N squares, 32N hexagons
Edges24N+48N
Vertices24N
Vertex figureSquare scalene, edge lengths 11 (base square), 2 (top edge), and 3 (sides)
Related polytopes
ArmyBatitit
RegimentBatitit
ConjugateNone
Abstract & topological properties
OrientableYes
Properties
SymmetryR5
ConvexYes
NatureTame

The bitruncated tesseractic tetracomb, or batitit, is a convex uniform tetracomb. 2 truncated hexadecachora and 4 tesseractihexadecachora join at each vertex of this tessellation. As the name suggests, it is the bitruncation of the tesseractic tetracomb.

## Vertex coordinates

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

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

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

## Representations

A bitruncated tesseractic tetracomb has the following Coxeter diagrams:

• o4x3x3o4o () (full symmetry)
• o3x3x4o *b3o () (half symmetry, rectangular scalene verf)
• x3x3o4o *b3x () (half symmetry, square pyramidal pyramid verf)
• x3x3x *b3o *b3o () (quarter symmetry, rectangular pyramidal pyramid verf)