Order-∞ apeirogonal tiling


The order-∞ apeirogonal tiling or infinite-order apeirogonal tiling is a paracompact regular tiling of the hyperbolic plane. Infinitely many apeirogons join at each vertex. It is self-dual and abstractly self-Petrial.

Order-∞ apeirogonal tiling
Rank3
Dimension2
TypeRegular, paracompact
SpaceHyperbolic
Notation
Bowers style acronymAzazat
Coxeter diagramx∞o∞o ()
Schläfli symbol{∞,∞}
Elements
Faces2N apeirogons
EdgesNM
Vertices2N
Vertex figureApeirogon, edge length 2
Petrie polygons2N zigzags
HolesN apeirogons
Measures (edge length 1)
Circumradius0
Related polytopes
ArmyAzazat
RegimentAzazat
DualOrder-∞ apeirogonal tiling
Petrie dualPetrial order-∞ apeirogonal tiling
φ 2 Order-∞ apeirogonal tiling
Abstract & topological properties
OrientableYes
Genus0
Properties
Symmetry[∞,∞]
ConvexYes

Representations Edit

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

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

External links Edit