Triangular tiling prism

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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[edit | edit source]

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

  • ,

where i  and j  range over the integers.

Integral coordinates can be given in 4 dimensions:

  • ,

where i  and j  range over the integers.

Representations[edit | edit source]

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 ()

External links[edit | edit source]