Order-∞ hexagonal tiling

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Order-∞ hexagonal tiling
Rank3
TypeRegular, paracompact
SpaceHyperbolic
Notation
Bowers style acronymAzhexat
Coxeter diagramo∞o6x ()
Schläfli symbol{6,∞}
Elements
FacesNM hexagons
Edges3NM
Vertices6N
Vertex figureApeirogon, edge length 3
Measures (edge length 1)
Circumradius
Related polytopes
ArmyAzhexat
RegimentAzhexat
DualOrder-6 apeirogonal tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[∞,6]
ConvexYes

The order-∞ hexagonal tiling or infinite-order hexagonal tiling is a paracompact regular tiling of the hyperbolic plane. Infinitely many ideal hexagons join at each vertex. All vertices are ideal points at infinity.

Representations[edit | edit source]

An order–∞ hexagonal tiling has the following Coxeter diagrams:

  • o∞o6x () (full symmetry)
  • x6o∞o6*a () (hexagons of two types)

External links[edit | edit source]

Template:O∞o6o6*a truncations