Category talk:Regular tessellations

I created this category because i couldn't find a list of regular honeycombs/tessellations across dimensions anywhere in Wikipedia -- even though there are many pages for specific regular tessellations/honeycombs, this information was scattered across various pages, and across various subsections of the very large and highly technical page https://en.wikipedia.org/wiki/List_of_regular_polytopes_and_compounds (and that page does not even define the term 'regular honeycomb' nor does it define 'regular tessellation', furthermore even in dimensions higher than 2 it alternates between the terms 'tessellation' and 'honeycomb' making it difficult to search for all information about honeycombs). Only when you put this information together in one list is the structure apparent; a self-dual hypercubic regular tessellation in every dimension, plus in dimensions 2 and 4, two other regular tessellations which are dual to each other.

There is a https://en.wikipedia.org/wiki/Template:Honeycombs, but it does not distinguish the regular honeycombs (nor does it note which are dual to each other).

There is a category 'Regular tilings' but the word 'tilings' usually refers just to 2-D, whereas 'tessellations' is more general. I originally was going to name this category 'Regular honeycombs' but that term is often used only for 3-D and up.

I think there should also be a page "regular tessellation". Currently that page redirects to https://en.wikipedia.org/wiki/Euclidean_tilings_by_convex_regular_polygons which is only talking about 2-D, and whose page text doesn't even contain the term "regular tessellation". The term "regular honeycomb" should also be redirected to "regular tessellation" once it is created. Currently that page redirects to https://en.wikipedia.org/wiki/List_of_regular_polytopes_and_compounds, which does mention the term "regular honeycomb", but does not define it. I think maybe the definition can currently be found on the page Honeycomb (geometry): "A honeycomb is called regular if the group of isometries preserving the tiling acts transitively on flags, where a flag is a vertex lying on an edge lying on a face lying on a cell." (provided that 'cell' is defined with sufficient generality, i guess?); that page also notes "Every regular honeycomb is automatically uniform."

Bayle Shanks (talk) 15:11, 19 February 2018 (UTC)