Apeirogonal dihedron

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Apeirogonal dihedron
Rank3
Dimension2
TypeRegular
SpaceEuclidean
Notation
Coxeter diagramx∞o2o ()
Schläfli symbol{∞,2}
Elements
Faces2 apeirogons
EdgesN 
VerticesN 
Vertex figureDigon
Petrie polygons2 apeirohedra
Related polytopes
ArmyAze
RegimentAze
DualApeirogonal hosohedron
Petrie dualApeirogonal dihedron
Abstract & topological properties
Flag count2N 
OrientableYes
Genus0
Properties
SymmetryW2×A1
ConvexYes
NatureWild

The apeirogonal dihedron is a degenerate regular tiling of the Euclidean plane.

Vertex coordinates[edit | edit source]

The vertex coordinates for the apeirogonal dihedron with unit edge length can be given as:

where i  is any integer.

Representations[edit | edit source]

An apeirogonal dihedron has the following Coxeter diagrams:

  • x∞o2o () (regular)
  • x∞x2o () (two alternating edge types)
  • s∞o2o () (as alternation)

External links[edit | edit source]