# 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

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:

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

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

## Representations

A truncated tesseractic tetracomb has the following Coxeter diagrams:

• x4x3o3o4o (full symmetry)
• o3o3o *b3x4x (half symmetry)

## Related polytopes

o4o3o3o4o truncations
Name OBSA CD diagram Picture
Tesseractic tetracomb test
Rectified tesseractic tetracomb rittit
Icositetrachoric tetracomb icot
Truncated tesseractic tetracomb tattit
Bitruncated tesseractic tetracomb batitit
Small rhombated tesseractic tetracomb srittit
Rectified icositetrachoric tetracomb ricot
Great rhombated tesseractic tetracomb grittit
Truncated icositetrachoric tetracomb ticot
Small prismated tesseractic tetracomb sidpitit
Prismatotruncated tesseractic tetracomb potatit
Prismatorhombated tesseractic tetracomb prittit
Great prismated tesseractic tetracomb gippittit
Tesseractic tetracomb test
Celliprismated tesseractic tetracomb capotat
Cellirhombated tesseractic tetracomb scartit
Celligreatorhombated tesseractic tetracomb gicartit
Celliprismatotruncated tesseractic tetracomb captatit
Great cellated tesseractic tetracomb otatit