Triangular prismatic honeycomb

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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[edit | edit source]

The vertices of a triangular prismatic honeycomb of edge length 1 are given by

  • ,

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

Representations[edit | edit source]

A triangular prismatic honeycomb has the following Coxeter diagrams:

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

External links[edit | edit source]