Talk:Tessellation

message: "It is possible to tessellate in non-Euclidean geometries such as hyperbolic geometry."
What about spherical geometry? Has nothing been done in this area? Is it somehow not possible due to a quirk of mathematics? I'd suggest at least a mention of this would be expected, since you mention the two other main branches of geometries.
--167.230.96.9 (talk) 20:58, 19 August 2015 (UTC)
replies: text: Agreed. Spherical polyhedron has regular, uniform, and uniform dual tilings of the sphere. These could be mentioned in Tessellation#Tessellations_in_non-Euclidean_geometries somewhere. And the regular 4-polytopes also can projected onto the 3-sphere as tessellations/honeycombs and viewed in stereographic projection. Like 120-cell projected here :File:Stereographic_polytope_120cell_faces.png. Tom Ruen (talk) 21:14, 19 August 2015 (UTC)

text: By loose analogy to the seventeen wallpaper groups, there is a family of tessellations of the sphere for each of the point groups in three dimensions. —Tamfang (talk) 09:53, 16 April 2023 (UTC)
thread_title:  Non-Euclidian Geometries -- Spherical Geometry? 

message: Substituted at 20:16, 1 May 2016 (UTC)
thread_title: Assessment comment

message: A nicely done "educational animation" was added by an anonymous user to "explain the basic principles behind tessellating patterns." I have removed it for a number of concerns.
# It introduces some artistic concepts about creating tessellation art, but does not really explain the basic idea of what a tessellation is. If the video is restored, perhaps it should go later in the article?
# The video ends with an ad for a certain website. This is not appropriate for the introduction to an article. Perhaps as an external link? I have not checked the website.
# It claims that only 3 "basic shapes" can tessellate. It is true that only 3 regular polygons tessellate, and many simple artistic tessellations follow these three patterns, but there are many other possible shapes and patterns in tessellations, such as the Arabic tessellation in the next image.
# The video claims there are 3 "basic principles" for tessellating: translation, rotation, glide reflection. Is reflection being considered a type of glide reflection? In any case, these are symmetries found in many (not all) tessellations, not "basic principles." E.g. Dirichlet tilings generally have no symmetry at all.
--seberle (talk) 06:19, 21 June 2016 (UTC)
replies: text: I agree with your decision to remove this animation. Any one of your four reasons would probably have been justification enough; the combination of all 4 makes the decision easy. Darrah (talk) 23:12, 22 June 2016 (UTC)

text: Nonkuli: The video is available on youtube here. There are hundreds of other similar videos that you can find with searches on youtube like "Tessellation Introduction", and if we were going to put one here, many of the other candidates do a better job of showing a wider variety of the basics, IMHO. Darrah (talk) 08:09, 21 August 2016 (UTC)
thread_title:  Introductory video 

message: The "In Manufacturing" section looks tiny. I think we should add more to this section.  — Preceding unsigned comment added by Jimli536 (talk • contribs) 23:23, 31 August 2016 (UTC)
thread_title:  Expand Manufacturing Section 

message: Tessellation currently seems a broad-concept article (BCA), covering several closely related concepts. Its main section, Tessellation#In mathematics, is notable enough to deserve a separate article, Tessellation (mathematics). That section is so large that it has its own introductory section. A summary of the new article would be left in the old section, of course. fgnievinski (talk) 05:45, 23 May 2021 (UTC)
replies: text: You know it's currently listed as a Good Article, correct? So perhaps your "this is all wrong and everyone who thinks otherwise is also wrong" approach could use re-thinking. Or in other words, what's wrong with an article that covers both the real-world and mathematical aspects of a topic, in a single article? Where is the need to ghettoize all mathematics into its own separate articles to keep them away from all those nasty real-world applications? To put it more bluntly, I strongly disagree. I think that having both applications and their mathematical analysis in a single article is a good thing. —David Eppstein (talk) 07:18, 23 May 2021 (UTC)
replies: text: I appreciate your concerns for ghettoization of mathematics. I believe it could be saned leaving a summary in the broad-concept article (BCA). That's how I and others have done at Surface and in Surface (mathematics). The intention here is more to give space for Tessellation (mathematics) to grow. Perhaps even have some equations (other than the few existing in-line equations), you know. But it looks like you prefer Tessellation not to be a WP:BCA, in which case the Mathematics subsections would be promoted and the Application sections demoted, as proposed in the second original option. fgnievinski (talk) 20:17, 23 May 2021 (UTC)
replies: text: Or, we could, you know, keep the balance as it already is and not do what you say or else. The threatening language you used as the header for this thread is not promising as a way of building consensus for some kind of change. —David Eppstein (talk) 20:55, 23 May 2021 (UTC)
replies: text: I apologize that my language made you feel threatened. That was not my intention, I value and expect civility in Wikipedia. So now I've rewritten the talk section title, replacing "or else" with "or an alternative". fgnievinski (talk) 23:28, 23 May 2021 (UTC)
thread_title:  Split "Tessellation (mathematics)" ― or an alternative 

message: There are article in New Scientist, but behind a paywall:
* 
jcubic (talk) 19:16, 2 April 2023 (UTC)
thread_title:  Infinite tessellation with single shape