Hexagonal prismatic honeycomb

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Hexagonal prismatic honeycomb
Rank4
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymHiph
Coxeter diagramxØo2x6o3o ()
Elements
CellsN hexagonal prisms
Faces3N squares, N hexagons
Edges2N+3N
Vertices2N
Vertex figureTriangular tegum, edge lengths 3 (equatorial) and 2 (sides)
Related polytopes
ArmyHiph
RegimentHiph
DualTriangular prismatic honeycomb
ConjugateNone
Abstract & topological properties
OrientableYes
Properties
SymmetryV3❘W2
ConvexYes
NatureTame

The hexagonal prismatic honeycomb, or hiph, is a convex noble uniform honeycomb. 6 hexagonal prisms join at each vertex of this honeycomb. It is the honeycomb product of the hexagonal tiling and the apeirogon.

This honeycomb can be alternated into a gyrated tetrahedral-octahedral honeycomb, which can be made uniform.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a hexagonal prismatic honeycomb of edge length 1 are given by:

  • ,
  • ,

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

Representations[edit | edit source]

A hexagonal prismatic honeycomb has the following Coxeter diagrams:

  • xØo2x6o3o ()
  • xØx2x6o3o ()
  • xØo2o6x3x ()
  • xØx2o6x3x ()
  • xØo2x3x3x3*c ()
  • xØx2x3x3x3*c ()

External links[edit | edit source]