# Hexagonal tiling prism

Hexagonal tiling prism
Rank4
TypeUniform
SpaceEuclidean
Notation
Coxeter diagramx6o3o2x ()
Elements
Cellshexagonal prisms, 2 hexagonal tilings
Faceshexagons, ∞ squares
Edges∞+∞
Vertices
Vertex figureTriangular pyramid
Related polytopes
ArmyHexagonal tiling prism
RegimentHexagonal tiling prism
Abstract & topological properties
OrientableYes
Properties
SymmetryV3×A1
ConvexYes
NatureTame

The hexagonal tiling prism is a prismatic uniform honeycomb of the Euclidean plane. It consists of 2 hexagonal tilings and ∞ hexagonal prisms. Each vertex joins 1 square tiling and 3 hexagonal prisms. It is a prism based on the hexagonal tiling.

## Vertex coordinates

A hexagonal tiling prism of edge length 1 has vertex coordinates given by, where ${\displaystyle i,\,j}$ range over the integers:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,3i\pm {\frac {1}{2}},\,{\sqrt {3}}j+{\frac {\sqrt {3}}{2}},\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,3i\pm 1,\,{\sqrt {3}}j,\,0\right)}$.

## Representations

A hexagonal tiling prism has the following Coxeter diagrams:

• x2x6o3o () (full symmetry)
• x2o6x3x () (as truncated triangular tiling prism)
• x2x3x3x3*b () (P3×A1 symmetry, as omnitruncated cyclotriangular tiling prism)
• x2s6x3x () (additional alternated faceting form)