# Hexagonal prismatic honeycomb

Hexagonal prismatic honeycomb Rank4
Typeuniform
SpaceEuclidean
Notation
Bowers style acronymHiph
Coxeter diagram         Elements
CellsN hexagonal prisms
Faces3N squares, N hexagons
Edges2N+3N
Vertices2N
Vertex figureTriangular tegum, edge lengths 3 (equatorial) and 2 (sides)
Related polytopes
ArmyHiph
RegimentHiph
DualTriangular prismatic honeycomb
ConjugateNone
Abstract & topological properties
OrientableYes
Properties
SymmetryV3❘W2
ConvexYes

The hexagonal prismatic honeycomb, or hiph, is a convex noble uniform honeycomb. 6 hexagonal prisms join at each vertex of this honeycomb. It is the honeycomb product of the hexagonal tiling and the apeirogon.

This honeycomb can be alternated into a gyrated tetrahedral-octahedral honeycomb, which can be made uniform.

## Vertex coordinates

Coordinates for the vertices of a hexagonal prismatic honeycomb of edge length 1 are given by:

• $\left(3i\pm\frac12,\,\sqrt3j+\frac{\sqrt3}{2},\,k\right),$ • $\left(3i\pm1,\,\sqrt3j,\,k\right),$ where i, j, and k range over the integers.

## Representations

A hexagonal prismatic honeycomb has the following Coxeter diagrams:

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