Truncated order-8 triangular tiling

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Truncated order-8 triangular tiling
Rank3
TypeUniform
SpaceHyperbolic
Notation
Bowers style acronymtotrat
Coxeter diagramo8x3x ()
Elements
Faces8N hexagons, 3N octagons
Edges12N+24N
Vertices24N
Vertex figureIsosceles triangle, edge lengths 2+2, 3, 3
Measures (edge length 1)
Circumradius
Related polytopes
ArmyTotrat
RegimentTotrat
DualOctakis octagonal tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[8,3]
ConvexYes

The truncated order-8 triangular tiling or totrat is a uniform tiling of the hyperbolic plane. 2 hexagons and 1 octagon join at each vertex. It can be formed from the truncation of the order-8 triangular tiling.

It is also the omnitruncate of the (4,3,3) family of tilings, with Coxeter diagram .

Representations[edit | edit source]

A truncated order-8 triangular tiling has the following Coxeter diagrams:

  • o8x3x () (full symmetry)
  • x3x4x3*a () (half symmetry)

External links[edit | edit source]