Prismatotruncated tesseractic tetracomb

Prismatotruncated tesseractic tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Potatit
Coxeter diagram	x4x3o3x4o ()
Elements
Tera	6N square-octagonal duoprisms, 4N cuboctahedral prisms, N rectified icositetrachora, N prismatorhombated hexadecachora
Cells	32N triangular prisms, 24N+24N cubes, 8N+16N cuboctahedra, 24N octagonal prisms, 4N truncated cubes
Faces	32N+64N triangles, 48N+96N+96N squares, 24N octagons
Edges	48N+96N
Vertices	32N
Vertex figure	Wedge pyramid, edge lengths 1 (two edges of base rectangle and top edge of wedge), √2 (sides of wedge, other edges of rectangle base, and lacings to rectangle), and √2+√2 (lacings to top edge)
Related polytopes
Army	Potatit
Regiment	Potatit
Conjugate	Quasiprismatotruncated tesseractic tetracomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5
Convex	Yes

The prismatotruncated tesseractic tetracomb or potatit, also called the runcitruncated tesseractic tetracomb is a convex uniform tetracomb. 1 rectified icositetrachoron, 2 prismatorhombated hexadecachora, 2 square-octagonal duoprisms, and 1 cuboctahedral prism join at each vertex of this tessellation. As the name suggests, it is the runcitruncation of the tesseractic tetracomb.

Vertex coordinates

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

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

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

Representations

A prismatotruncated tesseractic tetracomb has the following Coxeter diagrams:

• x4x3o3x4o (full symmetry)
• x3o3x *b3x4x (half symmetry)

External links

• Klitzing, Richard. "potatit".

• Wikipedia Contributors. "Runcitruncated tesseractic honeycomb".