# 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

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:

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

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)

## 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