# Triangular tiling prism

Triangular tiling prism
Rank4
TypeUniform
SpaceEuclidean
Notation
Coxeter diagramo6o3x2x ()
Elements
Cellstriangular prisms, 2 triangular tilings
Facestriangles, ∞ squares
Edges∞+∞
Vertices
Vertex figureHexagonal pyramid
Related polytopes
ArmyTriangular tiling prism
RegimentTriangular tiling prism
Abstract & topological properties
OrientableYes
Properties
SymmetryV3×A1
ConvexYes
NatureTame

The triangular tiling prism is a prismatic uniform honeycomb of the Euclidean plane. It consists of 2 triangular tilings and ∞ triangular prisms. Each vertex joins 1 square tiling and 6 triangular prisms. It is a prism based on the triangular tiling.

## Vertex coordinates

A triangular tiling prism of edge length 1 has vertex coordinates given by:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,i{\frac {\sqrt {3}}{2}},\,j+{\frac {i}{2}}\right)}$,

where i  and j  range over the integers.

Integral coordinates can be given in 4 dimensions:

• ${\displaystyle \left(i+j,i,j,{\dfrac {1\pm 1}{2}}\right)}$,

where i  and j  range over the integers.

## Representations

A triangular tiling prism has the following Coxeter diagrams:

• x2o6o3x () (full symmetry)
• x2x3o3o3*b () (P3×A1 symmetry, triangles considered of two types)
• x2s6o3o () (alternated hexagonal tiling prism)
• x2o6s3s ()
• x2s3s3s3*b ()