# Trihexagonal tiling prism

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

Trihexagonal tiling prism
Rank4
TypeUniform
SpaceEuclidean
Notation
Coxeter diagramo6x3o2x ()
Elements
Cellstriangular prisms, ∞ hexagonal prisms, 2 trihexagonal tilings
Facestriangles, ∞ squares, ∞ hexagons
Edges∞+∞
Vertices
Vertex figureRectangular pyramid
Related polytopes
ArmyTrihexagonal tiling prism
RegimentTrihexagonal tiling prism
Abstract & topological properties
OrientableYes
Properties
SymmetryV3×A1
ConvexYes
NatureTame

## Vertex coordinates

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

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