Alternated octagonal tiling


In geometry, the tritetragonal tiling or alternated octagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbols of or h.

Geometry

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

Triangle-centered
hyperbolic straight edges
Edge-centered
projective straight edges
Point-centered
projective straight edges

Dual tiling

In art

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.

Related polyhedra and tiling