Hexagonal prismatic honeycomb

Hexagonal prismatic honeycomb
Rank	4
Type	uniform
Space	Euclidean
Notation
Bowers style acronym	Hiph
Coxeter diagram
Elements
Cells	N hexagonal prisms
Faces	3N squares, N hexagons
Edges	2N+3N
Vertices	2N
Vertex figure	Triangular tegum, edge lengths √3 (equatorial) and √2 (sides)
Related polytopes
Army	Hiph
Regiment	Hiph
Dual	Triangular prismatic honeycomb
Conjugate	None
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	V3❘W2
Convex	Yes

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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External links

• Klitzing, Richard. "hiph".

• Wikipedia Contributors. "Hexagonal prismatic honeycomb".