Abstract:A self-affine tiling of a compact set G of positive Lebesgue measure is its partition to parallel shifts of a compact set which is affinely similar to G. We find all polyhedral sets (unions of finitely many convex polyhedra) that admit self-affine tilings. It is shown that in R d there exist an infinite family of such polyhedral sets, not affinely equivalent to each other. A special attention is paid to an important particular case when the matrix of affine similarity and the translation vectors are integer. A… Show more
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