Post #565993

There are a few different notations that are used to describe "regular" tilings (where we use "regular" in the informal sense of "simple arrangement of copies of a single shape"). The most important are probably Grünbaum and Shephard's incidence symbols for isohedral tilings, and Heesch and Kienzle's primitive tiling types. A system developed by Bigalke and Wippermann in the 1990s is intermediate between the other two. Talking to Doris Schattschneider last year, we realized that there doesn't seem to be a convenient cross reference online that shows how these systems relate to each other. So we created one: https://isohedral.ca/isohedral-tiles-tilings-and-notations/. We'll probably put this up on arXiv eventually, on the off chance that anybody wants to cite it. But the web page includes a few nice interactive features that give it independent value. We hope this is a useful resource!