# Triangular prismatic honeycomb

Triangular prismatic honeycomb
Rank4
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymTiph
Coxeter diagramxØo2x3o6o ()
Elements
Cells2N triangular prisms
Faces2N triangles, 3N squares
EdgesN+3N
VerticesN
Vertex figureHexagonal tegum, edge lengths 1 (equatorial) and 2 (sides)
Related polytopes
ArmyTiph
RegimentTiph
DualHexagonal prismatic honeycomb
ConjugateNone
Abstract & topological properties
OrientableYes
Properties
SymmetryV3❘W2
ConvexYes
NatureTame

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

• ${\displaystyle \left(i{\frac {\sqrt {3}}{2}},\,j+{\frac {i}{2}},\,k\right)}$,

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

## Representations

A triangular prismatic honeycomb has the following Coxeter diagrams:

• xØo2x3o6o ()
• xØx2x3o6o ()
• xØo2x3o3o3*c ()
• xØx2x3o3o3*c ()
• xØo2s3s3s3*c ()
• xØx2s3s3s3*c ()