The uniform locally finite tilings of the plane
The uniform locally finite tilings of the plane by finite combinatorial objects called labeling schemes are characterized. This representation is based on the analysis of the group of symmetries of a tiling which is realized independently of its geometry. It is shown that such tilings can be embedded in a geometry of the plane such that all tiles are regular polygons. As a consequence, it is given enumeration of all the uniform locally finite tilings having a given internal degree. It is also possible to decide whether or not there exists a tiling possessing a particular local geometric property.
scientific article; zbMATH DE number 5303720
scientific article