Triangular prismatic honeycomb

Triangular prismatic honeycomb
Rank	4
Type	uniform
Space	Euclidean
Notation
Bowers style acronym	Tiph
Coxeter diagram
Elements
Cells	2N triangular prisms
Faces	2N triangles, 3N squares
Edges	N+3N
Vertices	N
Vertex figure	Hexagonal tegum, edge lengths 1 (equatorial) and √2 (sides)
Related polytopes
Army	Tiph
Regiment	Tiph
Dual	Hexagonal prismatic honeycomb
Conjugate	None
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	V3❘W2
Convex	Yes

The triangular prismatic honeycomb, or tiph, is a convex noble uniform honeycomb. 12 triangular prisms join at each vertex of this honeycomb. As the name suggests, it is the honeycomb product of the triangular tiling and the apeirogon.

Vertex coordinates

The vertices of a triangular prismatic honeycomb of edge length 1 are given by

• $\left(i\frac{\sqrt3}{2},\,j+\frac{i}{2},\,k\right),$

where i, j, and k range over the integers.

Representations

A triangular prismatic honeycomb has the following Coxeter diagrams:

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External links

• Klitzing, Richard. "tiph".

• Wikipedia Contributors. "Triangular prismatic honeycomb".