Talk:Uniform tilings in hyperbolic plane

Missing image
Why is the image for "Order-5-4 rhombille tiling" missing? - dcljr (talk) 02:59, 4 September 2012 (UTC)
 * Found it! :) Tom Ruen (talk) 03:25, 21 January 2013 (UTC)

Possible Addition: Escher Art
A lot of Escher's art is based on tiling of the hyperbolic plane. It might be worthwhile to add links or images to his work. If you Google "escher tiling hyperbolic", you get many images of Escher's art. — Preceding unsigned comment added by MathPerson (talk • contribs) 16:05, 6 March 2013 (UTC)

what's active?

 * Each symmetry family contains 7 uniform tilings, defined by a Wythoff symbol or Coxeter-Dynkin diagram, 7 representing combinations of 3 active mirrors. An 8th represents an alternation operation, deleting alternate vertices from the highest form with all mirrors active.

"7 representing" and "active" are mysterious. —Tamfang (talk) 08:16, 13 October 2013 (UTC)


 * It definitely needs improvement, active meaning the generating point is off the mirror plane. This chart File:Wythoffian_construction_diagram.png shows the 7 generating positions for reflective symmetry. But then there are 1 to 7 more uniform tilings generated as alternations of the reflective 7, depending on which have all even-sided faces. Tom Ruen (talk) 07:59, 14 October 2013 (UTC)

Ideal quadrilateral domains?
Can quadrilateral domains have infinite elements?

Also, can you have pentagon domains? hexagon domains? octagon domains? infinite domains? 99.185.0.100 (talk) 14:46, 10 May 2015 (UTC)

Like these domains? Tom Ruen (talk) 17:46, 10 May 2015 (UTC)

Size (Browser / download size)
The article is quite large in Article size Browser-page size. ( the size in bytes of the page with all pictures included.)

Be careful I am not talking the Article sizeReadable-prose size or Wiki markup size. It is just this page contains a lot of pictures and takes long to load.

I think the page should therefore split up, but I have no idea yet on how to split it up. I think keep this article as a general page and then move the details to seperate pages, but what is general and what are the details? WillemienH (talk) 10:08, 26 July 2015 (UTC)


 * You could leave just one image in each main (level 2) section, and use "main" links to subsidiary articles, one per section. That would solve the load time problem.


 * I note in passing that the article gives the impression of completeness, but it seems there are many other possibilities, indeed (see item above) in some cases apparently infinite possibilities. If so, a small selection might be better (more compact, less misleading), together with some text explaining how other cases can be generated. I think David Eppstein might be able to advise you on this.


 * It is unclear, however, where the images come from, as there are no inline citations; it is more than possible that some of the images are wrongly drawn or wrongly labelled. A more robust action would be to remove or hide all unattributable images, and to source the rest (either to new, reliable sources, or to named pages or sections in the sources listed at the end of the article). This would make the article smaller and far more reliable, which readers might find an improvement. Chiswick Chap (talk) 10:40, 26 July 2015 (UTC)
 * When an article has the same content, less well organized, than the gallery pages for the corresponding Wikimedia commons categories, then we have a problem. I wouldn't be surprised if much of this material is original research (for instance, the catalogs of tilings for specific triangle groups: can these catalogs be found in the literature anywhere?). I suspect you will run into resistance from if you try to remove any of the galleries, though; that has been my experience with other articles that he has similarly cluttered up. —David Eppstein (talk) 17:09, 26 July 2015 (UTC)


 * The template tables of images could be made collapsible, and closed by default, but that might not help load time. The templates could also be given as links. The main value of them all together was to help show what uniform tilings exist as articles. Tom Ruen (talk) 17:19, 26 July 2015 (UTC)

For the moment I replaced all { { template tables } } with [ [template: template tables ] ] (links to the tables) not sure yet how further to reorganise the page, the whole representation needs improvement (more explanations) ideas welcome (as long as they lead to a much smaller Browser-page size than the original page. WillemienH (talk) 19:08, 19 September 2015 (UTC)

Regarding attempts to classify them by vertex configuration
There's this paper, but its definition is more restrictive than ours (e.g. 4.6.14 isn't allowed, because it has both left-handed and right-handed vertices). Double sharp (talk) 04:02, 26 August 2019 (UTC)
 * The latest version on the arxiv now allows such cases. :) Double sharp (talk) 09:02, 9 August 2022 (UTC)

Are there any non-Wythoffian tilings in hyperbolic plane?
There's a non-Wythoffian tiling in Euclidean plane (elongated triangular tiling). There's also (at least) one non-Wythoffian honeycomb in hyperbolic 3-space (partially diminished icosahedral honeycomb). Are there any non-Wythoffian tilings in hyperbolic plane? — Preceding unsigned comment added by 83.4.114.18 (talk) 10:30, 4 October 2019 (UTC)
 * Oh yes! Double sharp (talk) 06:30, 20 March 2020 (UTC)

Not all tessellations in this article are uniform
According to the article, the faces in these tilings are supposed to be regular polygons; however, plenty of them are seemingly not, for example the V3.3.3.3.3.4 tiling mentioned under Uniform tilings in hyperbolic plane, the V3.3.4.3.5 tiling mentioned under (5 4 2), the V3$4$.8 tiling under (8 3 2), and the V4.5.4.5 tiling under (5 5 2), as all of these have in common that each polygon shares some vertices with a certain number of other polygons, and other vertices with a different number of other polygons. This makes the angles differently large in different vertices, which makes the polygons non-regular. So if the tilings in this article are not all uniform, I think we need to figure out what they have in common and update the description of the article accordingly. —Kri (talk) 08:24, 20 January 2022 (UTC)
 * The ones starting with V are the duals of the uniform tilings. Double sharp (talk) 08:57, 9 August 2022 (UTC)

The table of Archimedean solids and tesselations goes offscreen on mobile browsers.
please fix this 37.48.48.145 (talk) 09:13, 21 February 2022 (UTC)