Talk:Trihexagonal tiling

Image removal
There's absolute no reason to exclude tiling images. I've done my best to keep it minimal.

These are expressed only in this article:
 * 1) Uniform colorings - belong here as symmetry variations
 * 2) Topologically identical tilings - belong here as geometric variations
 * 3) 2-uniform tilings - these belong here as more complex derived figures

Visual templates wiki-links for related articles:
 * 1) Related uniform tilings - Visually reference tilings of the same symmetry family
 * 2) Symmetry mutations - visually reference tilings of the same structure in different symmetry

Tom Ruen (talk) 16:06, 4 June 2015 (UTC)
 * My philosophy of a Wikipedia article is that it should be filled with prose, almost entirely about the topic of the article, with footnotes documenting that none of that prose is original research. Your philosophy of a Wikipedia article is that it should consist almost entirely of image galleries showing you all of the other articles you might want to look at instead of this one, all of which look identical because they're all filled with the same image galleries, with maybe a tiny amount of linking text thrown in to tell you where the article's subject sits in the middle of the grid of images about other things, and with some sources copied and pasted from the other articles that may or may not mention the subject but is sort of related to the same thing as the image galleries. I don't think that's a useful way to write an article. If you want to write a "list of..." article that's mostly an image gallery of the things it is supposed to be listing, fine. If an article about an actual specific topic (like the trihexagonal tiling) belongs to one of these lists, it should have a wikilink to that list. Only. No image gallery. No copy of the list in every article it lists. Just a wikilink. If you want to see related stuff, you can follow the wikilink. —David Eppstein (talk) 16:21, 4 June 2015 (UTC)


 * I understand we have different philosphies, but I don't see why they need to be in conflict. Some people are visual people, some are readers of prose. Articles can support both. If things are related visually, they should be expressed visually. I'm sure can improve the prose connected to the graphics. Weak writing skills is no reason for removal. Tom Ruen (talk) 16:28, 4 June 2015 (UTC)


 * Please stop removing. There are TWO small tables of images and wlinks. That's it! Tom Ruen (talk) 16:30, 4 June 2015 (UTC)
 * They belong elsewhere. They can go in a "list of..." article. We can include a LINK to that article here. This is not a "List of things sort of related to the trihexagonal tiling" article, it is an article that should be focused only on the trihexagonal tiling itself. As such, any "see also" type content should be minimized. The visual people can go to that other "list of..." article if that's what they want to see. Your galleries are making it impossible to find the actual content of the article because they are buried in a sea of images. And no, I will not stop removing, but see WP:3RR for limits on how often you should be reverting this removal. —David Eppstein (talk) 17:42, 4 June 2015 (UTC)


 * These are not lists. They are not distractions. They are centrally valuable and important visual comparisons. Please be specific. Which content in this article are you unable to find? Tom Ruen (talk) 17:46, 4 June 2015 (UTC)
 * A Wikipedia article should be mostly about the actual subject of the article. When the screen real estate devoted to stuff that's sort of like the subject but different and included only for navigational purposes to help you find that other stuff grows to more than say 1/3 of the total of the article, or even less for longer articles, you have a problem. In this case your current version has over 1/2 of the screen real estate about stuff that IS NOT THE TRIHEXAGONAL TILING. It does not belong here. It obscures the actual content. It is far far out of proportion to its importance to the subject. —David Eppstein (talk) 18:44, 4 June 2015 (UTC)


 * I understand that logic but disagree with the analysis of screen space and disagree that its clear how tightly focused an article must be based on a simple title. It is reasonable that material of closely related tilings be put here while each of those related tilings themselves don't deserve their own article. Which content is important to you here? Which content is getting lost for you here? How is expressing these relations diminishing that content? I'm always open to improvement, but I 100% disagree that things should be excluded on any objective grounds. It's all subjective, and so I'll compromise on presentation and what will help users, as I've tried to do. I don't know what criteria should lead to removing related material. Screen space is cheap, and has many ways to be organized to make everyone happy. Some material could go in a separate article, but having to click on a link to see a little table that takes a fraction of a screen would be annoying and unhelpful to readers in my opinion. Some tables might be collapsible for instance, but none are that big here. Tom Ruen (talk) 21:09, 4 June 2015 (UTC)

Removed material
All of this material was removed by David Eppstein, his fourth removal effort. His arguments are above, and I can't possibly agree with this removal. In my mind the connect between things is just as important as what things are, and pictures can be a 1000 words to people who want to see how things are connected.

If anyone else thinks this is important material to keep, perhaps they'll speak up? Tom Ruen (talk) 22:21, 5 June 2015 (UTC)


 * David Eppstein would like everyone to know I've motified on the contents below in small ways, as if improving material he doesn't like was a crime of deception. Here's actually what was removed for all who need clarity: (historical version ) Tom Ruen (talk) 02:40, 6 June 2015 (UTC)

Symmetry
There are eight uniform tilings based on Wythoff constructions from the regular hexagonal tiling. The truncated triangular tiling, t{3,6} is topologically equivalent to the hexagonal tiling. The vertices of the trihexagonal tiling are positioned at the mid-edges of both the hexagonal tiling and the triangular tiling.

Circle packing
The trihexagonal tiling or kagome lattice can be used as a periodic circle packing, placing equal diameter circles at the center of every vertex. This circle packing is not a true lattice because there are 3 circle positions within each lattice cell. Every circle is in contact with 4 other circles in the packing (kissing number). The gap inside each hexagon allows for one circle, creating the densest packing from the triangular tiling, with each circle contact with the maximum of 6 circles.

Symmetry mutations
The trihexagonal tiling is a series of symmetry mutations of quasiregular tilings sharing with vertex configurations (3.n)2, moving from the sphere to the Euclidean plane and into the hyperbolic plane. All of these tilings are identical colorings of their fundamental domain of symmetry, with orbifold notation *n32.

Comments

 * To clarify my reasoning:
 * Links to other subjects should be made by wikilinks, not by importing and copying the content of those other subjects here and to every other subject they are linked to; this applies to the images of hexagonal tilings. Otherwise, what is the point of having separate articles?
 * I have no idea what it is supposed to mean that one uniform tiliing is "exactly between" two other uniform tilings, and that sentence was in any case unsourced.
 * The circle packing section is pointless and inane (yes, you can pack circles on these points; so what), the claim about being the second-densest packing is wrong as stated (denser: use the triangular tiling one but space the circles at slightly greater than unit distance), no source was given, and the sources I did find (e.g. Wells' book) say absolutely nothing about the trihexagonal tiling, but rather refer to uniform tilings more generally, leading me to believe if this material is to be included then the proper place for it is the uniform tilings article, not here. If you want to connect circle packings to this tiling, look instead at its dual and at the following paper of mine:.
 * The symmetry mutation part is horribly sourced (search engine results are unacceptable), mathematical gibberish (what does it mean for a tiling to be moving? why did you use the word "series" instead of "sequence"? in what sense is a tiling a coloring?), and again the table of images duplicates content that should be in another wikilinked article. —David Eppstein (talk) 22:34, 5 June 2015 (UTC)
 * —David Eppstein (talk) 22:34, 5 June 2015 (UTC)
 * Additionally I would like to point out that Tomruen has edited the above "removed material" to add content and sources that were not there when I removed it. So the claim that this is the material I removed is a lie. —David Eppstein (talk) 01:22, 6 June 2015 (UTC)
 * You're the feisty one. If I can't improve content in the article, I'll improve it here while I'm waiting if anyone cares. They can look at the history if I'm "lying", or if you change your mind by my improvements you can move it back. Tom Ruen (talk) 02:34, 6 June 2015 (UTC)

Today's removal
I removed the following section as original research. In this case, the material looks on-topic and the images are not excessive. And the sources given are adequate to prove the existence and 2-uniformity of these three tilings. However, they do not single them out as a group nor do they source any relationship between these tilings and the trihexagonal tiling. We need sources saying not only that the tilings exist, but that they are connected to the trihexagonal tiling, in order to say in our article that they are connected. And if we can't say they are connected, there is no point in including them. —David Eppstein (talk) 18:56, 6 June 2015 (UTC)


 * They are related in exactly the same way as the icosidodecahedron, but I don't have an explicit source so far: Tom Ruen (talk) 19:17, 6 June 2015 (UTC)
 * You should not have been adding content that you do not already have sources for. When you do, it is original research. —David Eppstein (talk) 20:16, 6 June 2015 (UTC)
 * The current mystery to me is why a "gyroelongation" (elongating by an infinite antiprism triangles) isn't a 2-uniform tiling, similar to the Johnson solid gyroelongated pentagonal birotunda. Anyway, no one has bothered to enumerate the convex k-uniform polyhedra to my knowledge, although they must all be Johnson solids. Tom Ruen (talk) 20:30, 6 June 2015 (UTC)
 * p.s. The 2 variations of gyroelongations are listed as 3-uniform (34.6; 34.6; (3.6)2) in Tilings by regular polygons II p.157. Darn those symmetry orbits of chiral tilings. Tom Ruen (talk) 20:59, 6 June 2015 (UTC)

Related k-uniform tilings
There are 3 related 2-uniform tilings (having two types of vertices), and 5 related 3-uniform tilings. All 9 tilings contain 3.6.3.6 vertices. The first tiling offsets rows of hexagons of the trihexagonal tiling changing half of the 3.6.3.6 vertices into 3.3.6.6. The other two are elongations of those two, inserting an infinite prism, and separating 3.6.3.6 or 3.3.6.6 vertices into 3.6.4.4. Similarly there are 3 tilings with only alternate rows elonagated or offset, with 2 vertex types, but being 3-uniform. Finally two gyorelongated forms extend the first two by triangles as infinite antiprisms, have two types of vertices, but 3 symmetry orbits, so they are 3-uniform.

The offset and elongated offset tilings 2-uniform tilings are similar to the leno weave, each has sets of one or two straight parallel lines and in one direction and two curves alternating positions in the perpendicular direction.

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