Talk:Rhombille tiling

Quasiregular duals

As I understand quasiregularity, these figures are duals to quasiregular figures, they are not themselves quasiregular. See Quasiregular polyhedron. Or, do all the references gven use quaisiregularity in the sense used here? Either way, I think Wkipedia should be consistent between articles. -- Cheers, Steelpillow (Talk) 08:09, 7 July 2009 (UTC)[reply]

The dual usage of quasiregular is expressed in the polyhedron article, but basically Cromwell is the only reference I have that with this dual usage, with edge-transitivity the common property. I don't know what the tiling should be renamed to. rhombic tiling can also refer to a vector-space rhombic lattice [1]. Conway offered his own name in Symmeties of things. There's also the hyperbolic rhombic forms. It could be given more descriptively as dual trihexagonal tiling or Order 3-6 rhombic tiling? Tom Ruen (talk) 01:30, 8 July 2009 (UTC)[reply]

In that case, I would suggest that this tiling has never gained an established name because it is no significant enough to be worth it. So it seems to me that the present material has neither sufficient mathematical significance nor sufficient size to warrant its own article:

The current title creates a de facto name for the tiling, which breaks WP:NOR.
The "related" material is equal to the relevant stuff, and belongs in its own article.
What is left is too skimpy to be a full article. Padding it out with trivial details would fall foul of WP:NOTDIRECTORY.
It is also not notable and breaches WP:GNG - for example none of the references treats this tiling with any great significance.

In short, I now think this article should be deleted. Frankly, many of the individual polytope and tiling articles fail one or more of these criteria too, and should go the same way. All the salient information is contained in more general articles listing them all. -- Cheers, Steelpillow (Talk) 11:26, 8 July 2009 (UTC)[reply]

The only other place currently that it is given is at List of uniform tilings. My thought is that if some of the (uniform+dual) polyhedra/polytopes/tilings/honeycombs are given, and there's a relatively small and finite number, its valuable to have them all. Value seems in the eye of the beholder. Coxeter got interested in nonconvex uniform polyhedra and duals, and they were all named, but simpler, nicer uniform tilings were neglected. I'd dump the confusing nonconvex polyhedra before I'd dump the simple tilings, BUT I'd not dump any as long as someone values them. Tom Ruen (talk) 19:48, 8 July 2009 (UTC)[reply]

Whether someone values them and whether they violate policy are different issues. As you say, "Value seems in the eye of the beholder", while Wikipedia policy may be found here. Many things that people value are banned by WP:NOT. One option might be to move the content to an article about the relationship described between this and other polyhedra, and reformat it accordingly. I notice that this is not the only article with little to say about its titular tiling and more to say about a relationship between several figures. Meanwhile, since Conway has named these tilings in print, you should at least use his names and abandon your WP:OR. -- Cheers, Steelpillow (Talk) 20:21, 8 July 2009 (UTC)[reply]

I expanded the article contents, again as you say, relationships which to me is very important, and what can't be organized as well without individual articles. As far as Conway's names, I'm glad for them, but not entirely satisfied by them, prefer descriptive names for articles to shorter names that are not widely standard. Tom Ruen (talk) 22:17, 8 July 2009 (UTC)[reply]

Given that Cromwell's definition of quasiregularity is even less standard than Conway's published works, by your own argument this article should be retitled Quadrille tiling. However, since you have expanded and refocussed its scope to such an extent, I think that Rhombic tilings might be better. It certainly cannot stay as it is. -- Cheers, Steelpillow (Talk) 19:17, 9 July 2009 (UTC)[reply]

What it is mean?

Sentence in article: It is possible to embed the rhombille tiling into a subset of a three-dimensional integer lattice, consisting of the points (x,y,z) with |x + y + z| ≤ 1, ...

Something wrong... |x + y + z| ≤ 1 gives only 3 points - (1, 0, 0), (0, 1, 0) and (0, 0, 1). How we can embed infinit tiling in three points? Jumpow (talk) 18:06, 11 March 2016 (UTC)[reply]

The coordinates are allowed to be outside the range (0,1). So for instance (4,-9,6) would also be allowed. —David Eppstein (talk) 19:49, 12 March 2016 (UTC)[reply]