- A tessellation has a meaning in mathematics. See wiktionary definition.A tessellation is a type of tiling. Hence tessellation such be in the category tiling. Gordo (talk) 13:24, 22 August 2013 (UTC)
- As noted in the book "Tilings and Patterns" by Grünbaum and Shephard,
In mathematical literature, the words tessellation, paving, mosaic and parquetting are used synonymously or with similar meanings. The German words for tiling are Pflasterung, Felderung, Teilung, Parkettierung and Zerlegung. The French words are pavage, carrelage and dallage. The Russian words are паркетаж, разбиение and замощение.
—Grünbaum, Branko; Shephard, G. C., Tilings and Patterns, p.16
- I agree with Stannic and I too am horrified to see Wikitionary cited as a reliable source.
- One may also recall Grünbaum's Uniform Tilings of 3-space, which addresses certain tessellations also frequently referred to as honeycombs. Mathematically all these terms are quite interchangeable although, as Grünbaum's usage demonstrates, the term "tilings" has come to be favoured as the root class. For another example, observe that mathematicians do not talk of "Penrose tessellations" but rather of "Penrose tilings."
- In common usage too the term "tilings" is pretty much universal. Nobody talks of different "tessellations" for their bathroom wall. The term "tessellation" originated in the learned description of Classical era mosaic construction and not in mathematics.
- One needs a root or top-level Category, and "Tilings" is the obvious one. Does one then need specialist sub-categories? Well, yes if the sub-category is a sub-class of object, such as tilings of the plane, but not if it is just a synonym. The present unsatisfactory situation both here and on Wikipedia is that editors have been picking and choosing different synonyms in order to distinguish one editor's choice from another without any real attempt at rigour, and selectively citing references to back their claims when contrary references (such as the above quote) also exist. This needs to stop. There is no accepted mathematical distinction between tiling and tessellation, but if one exists in say archaeology or Classical literature then fine, keep the Category, but otherwise let's use the word that English speakers habitually use and get rid of the pseudo-mathematical misunderstandings.
- — Cheers, Steelpillow (Talk) 14:32, 22 August 2013 (UTC)
My impression is also that, in mathematical parlance, "tessellation" and "tiling" are synonymous. But "tiling" also has the real-world meaning of covering a surface by physical tiles, so I think keeping the mathematical meaning at "tesselations", as it is now, is helpful in avoiding ambiguity. Many of its subcategories use "tiling" instead of "tessellation", but so what? —David Eppstein (talk) 19:54, 24 August 2013 (UTC)
- "Tessellation" also has real-world origins in constructing mosaics. My old Chambers 20th Century dictionary gives only the real-world definition, with a bare and inadequate hint at geometry; "marked out in little squarish areas". So I would suggest that we cannot restrict "tessellation" to its mathematical meaning any more than we can restrict "tiling". I would suggest that using same word consistently throughout the hierarchy of category names would be a better way to reduce confusion. If we wish to split off a dedicated mathematical category then say Category:Mathematical tilings or Category:Tilings (mathematics) would be less ambiguous than the current name. — Cheers, Steelpillow (Talk) 11:04, 25 August 2013 (UTC)
- In earlier discussion it was noted that mathematical tilings should not be separated from real ones, and so categories like "Category:Tilings (geometry)" or "Category:Tilings in geometry" should not be used because all real-world tilings are mathematical too. So if there is need in dedicated mathematical category, then why, and what images would belong there? Or, putting question other way — what images would not belong there? — Stannic (talk) 14:37, 25 August 2013 (UTC)