Truncated square tiling

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Truncated square tiling
Rank3
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymTosquat
Coxeter diagramx4x4o ()
Elements
FacesN squares, N octagons
Edges2N+4N
Vertices4N
Vertex figureIsosceles triangle, edge lengths 2, 2+2, 2+2
Measures (edge length 1)
Vertex density
Related polytopes
ArmyTosquat
RegimentTosquat
DualTetrakis square tiling
ConjugateQuasitruncated square tiling
Abstract & topological properties
Flag count24N
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryR3
ConvexYes
NatureTame

The truncated square tiling, or tosquat, is one of the eleven convex uniform tilings of the Euclidean plane. 1 square and 2 octagons join at each vertex of this tiling. As its name suggests, it is the truncation of the regular square tiling.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a truncated square tiling of edge length 1 are given by all permutations of

  • ,

where i  and j  range over the integers.

Representations[edit | edit source]

A truncated square tiling has the following Coxeter diagrams:

  • x4x4o () (maximum symmetry)
  • x4x4x () (as omnitruncated square tiling)
  • s4o4x () (as alternated facting)
  • s4x4x ()

External links[edit | edit source]