Tiling
A tiling T in Rd is a countable set of tiles, which is a covering as well as a packing of Rd. I.e., the union of all tiles in T is Rd, and the intersection of the interior of two different tiles in T is empty.
If T contains only finitely many congruence classes of tiles (resp. translation classes), then a family {T1, T2 ... Tm} of representants of each class is called the family of prototiles. With the help of these prototiles, T can be written as T={ fi (Tj(i)) | fi isometries, i=1,2,3... }. In the case of finitely many prototiles up to translation one has an even simpler representation, namely T={ Tj(i) + xi | i=1,2,3...}.
Synonyms
mosaic, parquetting, paving, tessellation
Page Authors
2006-01-17 D. Frettlöh
»
