Heesch's Tiling Problem

Mann presents a solution to Heinrich Heesch's Tiling Problem, which was stated in 1968, and is connected to another unsolved tilting problem that is central to the subject. He introduces a few families of tiles with Heesch numbers 3, 4, and 5, as well as other examples. Furthermore, Heesch'...

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Bibliographic Details
Published inThe American mathematical monthly Vol. 111; no. 6; pp. 509 - 517
Main Author Mann, Casey
Format Journal Article
LanguageEnglish
Published Washington Taylor & Francis 01.06.2004
Mathematical Association of America
Taylor & Francis Ltd
Subjects
Geometric planes
Geometry
Heesch, Heinrich
Hexagons
Mathematical analysis
Mathematical theorems
Numbers
Polygons
Tessellations
Tiles
Tiling
Vertices
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Summary:Mann presents a solution to Heinrich Heesch's Tiling Problem, which was stated in 1968, and is connected to another unsolved tilting problem that is central to the subject. He introduces a few families of tiles with Heesch numbers 3, 4, and 5, as well as other examples. Furthermore, Heesch's tiling problem can be posed for protosets containing more than one prototile and for a starting configuration to be surrounded in which it comprises of more than one tile.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2004.11920105