Prismatorhombated tesseractic tetracomb

Prismatorhombated tesseractic tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Prittit
Coxeter diagram	x4o3x3x4o ()
Elements
Tera	6N tesseracts, 4N truncated octahedral prisms, N tesseractihexadecachora, N prismatorhombated tesseracts
Cells	24N+24N cubes, 32N hexagonal prisms, 16N truncated tetrahedra, 4N cuboctahedra, 8N truncated octahedra
Faces	32N triangles, 24N+24N+48N+96N squares, 64N hexagons
Edges	96N+96N+96N
Vertices	96N
Vertex figure	Isosceles trapezoidal scalene, base edge lengths 1, √2, √2, √2, opposite edge length √2, lacing lengths √2 and √3
Related polytopes
Army	Prittit
Regiment	Prittit
Conjugate	Quasiprismatorhombated tesseractic tetracomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5
Convex	Yes

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:

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

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)

External links

• Klitzing, Richard. "prittit".

• Wikipedia Contributors. "Runcicantellated tesseractic honeycomb".