# Alternated octagonal tiling

(Redirected from Tritetragonal tiling)
Alternated octagonal tiling

Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration (3.4)3
Schläfli symbol (4,3,3)
s(4,4,4)
Wythoff symbol 3 | 3 4
Coxeter diagram
Symmetry group [(4,3,3)], (*433)
[(4,4,4)]+, (444)
Dual Alternated octagonal tiling#Dual tiling
Properties Vertex-transitive

In geometry, the tritetragonal tiling or alternated octagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbols of {(4,3,3)} or h{8,3}.

## Geometry

Although a sequence of edges seem to represent straight lines (projected into curves), careful attention will show they are not straight, as can be seen by looking at it from different projective centers.

 Triangle-centeredhyperbolic straight edges Edge-centeredprojective straight edges Point-centeredprojective straight edges

## In art

Circle Limit III is a woodcut made in 1959 by Dutch artist M. C. Escher, in which "strings of fish shoot up like rockets from infinitely far away" and then "fall back again whence they came". White curves within the figure, through the middle of each line of fish, divide the plane into squares and triangles in the pattern of the tritetragonal tiling. However, in the tritetragonal tiling, the corresponding curves are chains of hyperbolic line segments, with a slight angle at each vertex, while in Escher's woodcut they appear to be smooth hypercycles.