Euclidean tilings by convex regular polygons: Difference between revisions

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Convex regular polygons can also form plane tilings that are not edge-to-edge. Such tilings can be considered edge-to-edge as nonregular polygons with adjacent colinear edges.

There are seven families of [[isogonal figure|isogonal]] each family having a real-valued parameter determining the overlap between sides of adjacent tiles or the ratio between the edge lengths of different tiles. Two of the families are generated from shifted square, either progressive or zig-zagging positions. Grünbaum and Shephard call these tilings ''uniform'' although it contradicts Coxeter's definition for uniformity which requires edge-to-edge regular polygons.<ref>[{{Cite web |url=http://www.maa.org/sites/default/files/images/upload_library/22/Allendoerfer/1978/0025570x.di021102.02p0230f.pdf |title=Tilings by regular polygons] |p.=236 |archive-url=https://web.archive.org/web/20160303235526/http://www.maa.org/sites/default/files/images/upload_library/22/Allendoerfer/1978/0025570x.di021102.02p0230f.pdf |archive-date=2016-03-03 |url-status=dead}}</ref> Such isogonal tilings are actually topologically identical to the uniform tilings, with different geometric proportions.

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