Quasitruncated square tiling

Quasitruncated square tiling
Rank	3
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Quitsquat
Coxeter diagram	x4/3x4o ()
Elements
Faces	N squares, N octagrams
Edges	2N+4N
Vertices	4N
Vertex figure	Isosceles triangle, edge lengths √2, √2-√2, √2-√2
Related polytopes
Army	Tosquat
Regiment	Quitsquat
Conjugate	Truncated square tiling
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R3
Convex	No
Nature	Tame

The quasitruncated square tiling, or quitsquat, is a non-convex uniform tiling of the Euclidean plane. 1 square and 2 octagrams join at each vertex of this tiling. It can be formed by quasitruncation of the regular square tiling, with the squares seen as 4/3-gons.

Vertex coordinates

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

• $\left(\pm {\frac {1}{2}}+({\sqrt {2}}-1)i,\,\pm {\frac {{\sqrt {2}}-1}{2}}+j({\sqrt {2}}-1)\right),$

where i and j range over the integers.

Representations

A quasitruncated square tiling has the following Coxeter diagrams:

• x4/3x4o (- ) (regular)
• x4/3x4/3o () (retrograde)
• x4/3x4/3x () (octagrams of two types)

External links

• Klitzing, Richard. "quitsquat".
• McNeill, Jim. "Star Tesselations Type 10".