Octagonal tiling

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Octagonal tiling
Rank3
TypeRegular
SpaceHyperbolic
Notation
Bowers style acronymOcat
Coxeter diagramx8o3o ()
Schläfli symbol{8,3}
Elements
Faces3N octagons
Edges12N
Vertices8N
Vertex figureTriangle, edge length 2+2
Measures (edge length 1)
Circumradius
Related polytopes
ArmyOcat
RegimentOcat
DualOrder-8 triangular tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[8,3]
ConvexYes

The order-3 octagonal tiling, or just octagonal tiling, is a regular tiling of the hyperbolic plane. 3 octagons join at each vertex.

It can be formed by truncating the order-8 square tiling.

Representations[edit | edit source]

The octagonal tiling has the following Coxeter diagrams:

  • x8o3o () (main symmetry)
  • o8x4x () (as truncated order-8 square tiling)
  • x4x4x4*a () (octagons of three types)

External links[edit | edit source]