Order-6 apeirogonal tiling

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Order-6 apeirogonal tiling
H2 tiling 26i-1.png
Rank3
TypeRegular, paracompact
SpaceHyperbolic
Notation
Bowers style acronymHazat
Coxeter diagramx∞o6o (CDel node 1.pngCDel infin.pngCDel node.pngCDel 6.pngCDel node.png)
Schläfli symbol{∞,6}
Elements
Faces6N apeirogons
Edges3NM
VerticesNM
Vertex figureHexagon, edge length 2
Measures (edge length 1)
Circumradius
Related polytopes
ArmyHazat
RegimentHazat
DualOrder-∞ hexagonal tiling
Topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[∞,6]
ConvexYes


The order-6 apeirogonal tiling is a paracompact regular tiling of the hyperbolic plane. 6 apeirogons join at each vertex.

Representations[edit | edit source]

The order-6 apeirogonal tiling has the following Coxeter diagrams:

  • x∞o6o (full symmetry)
  • o3o∞x∞*a (apeirogons of two types)

Related polytopes[edit | edit source]

o∞o6o truncations
Name OBSA Schläfli symbol CD diagram Picture
Order-6 apeirogonal tiling hazat {∞,6} CDel node 1.pngCDel infin.pngCDel node.pngCDel 6.pngCDel node.png
H2 tiling 26i-1.png
Truncated order-6 apeirogonal tiling thazat t{∞,6} CDel node 1.pngCDel infin.pngCDel node 1.pngCDel 6.pngCDel node.png
H2 tiling 26i-3.png
Hexaapeirogonal tiling hazt r{∞,6} CDel node.pngCDel infin.pngCDel node 1.pngCDel 6.pngCDel node.png
H2 tiling 26i-2.png
Truncated order-∞ hexagonal tiling tazhat t{6,∞} CDel node.pngCDel infin.pngCDel node 1.pngCDel 6.pngCDel node 1.png
H2 tiling 26i-6.png
Order-∞ hexagonal tiling azhat {6,∞} CDel node.pngCDel infin.pngCDel node.pngCDel 6.pngCDel node 1.png
H2 tiling 26i-4.png
Small rhombihexaapeirogonal tiling srohazt rr{∞,6} CDel node 1.pngCDel infin.pngCDel node.pngCDel 6.pngCDel node 1.png
H2 tiling 26i-5.png
Great rhombihexaapeirogonal tiling grohazt tr{∞,6} CDel node 1.pngCDel infin.pngCDel node 1.pngCDel 6.pngCDel node 1.png
H2 tiling 26i-7.png
Snub hexaapeirogonal tiling sr{∞,6} CDel node h.pngCDel infin.pngCDel node h.pngCDel 6.pngCDel node h.png
H2 snub 26ia.png

External links[edit | edit source]