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WikiProject Mathematics (Rated GA-class, Mid-importance)
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One of the 500 most frequently viewed mathematics articles.

Non-Euclidian Geometries -- Spherical Geometry?[edit]

"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.
-- (talk) 20:58, 19 August 2015 (UTC)

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)

Assessment comment[edit]

The comment(s) below were originally left at Talk:Tessellation/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

At present this is largely a random collection of a few specific topics. It needs going through with reference to Tilings and Patterns to make sure that all the main topics and terminology are covered in a coherent arrangement; in the process, most of the "See also" links should become links at appropriate points in the body of the article instead. Joseph Myers 02:20, 20 May 2007 (UTC)

Last edited at 02:20, 20 May 2007 (UTC). Substituted at 20:16, 1 May 2016 (UTC)

Introductory video[edit]

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.

  1. 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?
  2. 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.
  3. 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.
  4. 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)

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)

I'd really love to see that video. Too bad it has been removed Nonkuli (talk) 13:11, 13 August 2016 (UTC)

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)

Expand Manufacturing Section[edit]

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