# Prismatorhombated tesseractic tetracomb

Prismatorhombated tesseractic tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymPrittit
Coxeter diagramx4o3x3x4o ()
Elements
Tera6N tesseracts, 4N truncated octahedral prisms, N tesseractihexadecachora, N prismatorhombated tesseracts
Cells24N+24N cubes, 32N hexagonal prisms, 16N truncated tetrahedra, 4N cuboctahedra, 8N truncated octahedra
Faces32N triangles, 24N+24N+48N+96N squares, 64N hexagons
Edges96N+96N+96N
Vertices96N
Vertex figureIsosceles trapezoidal scalene, base edge lengths 1, 2, 2, 2, opposite edge length 2, lacing lengths 2 and 3
Related polytopes
ArmyPrittit
RegimentPrittit
ConjugateQuasiprismatorhombated tesseractic tetracomb
Abstract & topological properties
OrientableYes
Properties
SymmetryR5
ConvexYes
NatureTame

The prismatorhombated tesseractic tetracomb or prittit, also called the runcicantellated tesseractic tetracomb is a convex uniform tetracomb. 1 tesseractihexadecachoron, 2 prismatorhombated tesseracts, 1 truncated octahedral prism, and 1 tesseract (as a square duoprism) join at each vertex of this tessellation. As the name suggests, it is the runcicantellation of the tesseractic tetracomb.

## Vertex coordinates

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

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

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

## Representations

A prismatorhombated tesseractic tetracomb has the following Coxeter diagrams:

• x4o3x3x4o (full symmetry)
• x3x3x *b3o4x (half symmetry)