# Prismatotruncated tesseractic tetracomb

Prismatotruncated tesseractic tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymPotatit
Coxeter diagramx4x3o3x4o ()
Elements
Tera6N square-octagonal duoprisms, 4N cuboctahedral prisms, N rectified icositetrachora, N prismatorhombated hexadecachora
Cells32N triangular prisms, 24N+24N cubes, 8N+16N cuboctahedra, 24N octagonal prisms, 4N truncated cubes
Faces32N+64N triangles, 48N+96N+96N squares, 24N octagons
Edges48N+96N
Vertices32N
Vertex figureWedge 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
ArmyPotatit
RegimentPotatit
ConjugateQuasiprismatotruncated tesseractic tetracomb
Abstract & topological properties
OrientableYes
Properties
SymmetryR5
ConvexYes
NatureTame

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:

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

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

## Representations

A prismatotruncated tesseractic tetracomb has the following Coxeter diagrams:

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