# Category talk:Tilings-db

## Categorising tilings

Things are not as simple as you seem to think. I would strongly suggest that you need to get your categories reviewed and agreed before you go any further, and then take great care in assigning them to any given tiling.

Categorisation by topological space.
• Missing from here are tilings of the projective plane. It might be useful to rename Category:Plane tilings to say Category:Euclidean plane tilings.
• Tilings of 3-space and higher spaces also need to be disambiguated in the naming system, for example tilings of hyperbolic space - and higher dimensions - as distinct from tilings of the hyperbolic plane. They are sometimes called honeycombs rather than tilings, but this is not universal and usages of the term "honeycomb" differ. "Tiling" is the correct umbrella technical term.
Categorisation by degree of regularity
Isohedral (same-faced), isogonal (same-cornered), isotoxal (same-edged) and related symmetry classes such as Quasiregular and Noble tilings need their own categories. Great care is needed, for example a noble tiling is both isogonal and isohedral but not necessarily isotoxal, while a quasiregular tiling is isogonal and isotoxal but not isohedral - this last property can be affected by colouring the faces, for example a tiling of squares is regular but a chequerboard is quasiregular. Worse, a tiling of parallel-oriented diamonds is isogonal, isotoxal and isohedral but is neither regular nor quasiregular.

— Cheers, Steelpillow (Talk) 13:29, 17 August 2013 (UTC)

I assumed that the current categorization will cover all or most tilings already uploaded and is plain enough (i.e., it is possible to categorize tilings with few basic categories and then add more complex ones gradually).
Some categories have not absolutely correct names, too (for example, instead of "Category:Hyperbolic tilings with squares" it would be better to use "Category:Uniform hyperbolic tilings with squares", etc.)
You are also right that colorings are ignored by current categorization. However, under many uploaded images there are links "equivalent" and "dual", e.g. two pictures on the right, and these links seem to count differently colored tilings as equivalent too.
As you have pointed out, good categorization is not simple, so I wanted to build most basic one, and I do not see why it is incorrect. If something is totally incorrect here then I'll stop and wait for other comments.
Thanks, Stannic (talk) 15:03, 17 August 2013 (UTC)
To take your points in order.
You have not addressed the issue of naming categories for higher-dimensional tilings, of which there are plenty already uploaded. If you ignore such issues now, you may find a lot of changes needed down the line.
Incorrect category names simply mean that the images need moving to the correct category. For example Category:Dual uniform tilings‎ would more usually be phrased as Category:Uniform dual tilings‎.
More immediately, it is not adequate or correct to treat "plane" as meaning "Euclidean plane". Many seekers of say hyperbolic plane tilings will rightly assume that Category:Plane tilings‎ is a sensible place to start looking, so it needs to be. You really do need a Category:Euclidean tilings‎.
Spherical tilings are also called spherical polyhedra, so there is a debate to be had there as well.
Colourings. There is a distinction between a tiling coloured to make it look pretty and a tiling which is mathematically coloured so that tiles of different colours are treated as belonging to different groups. Just because one wikipedia editor takes a given view does not mean that it is the correct one. You show two images of hyperbolic octagonal tilings. If we ignore the colouring they are the same tiling, if we take the colouring into account they are different tilings with different symmetries. Sometimes this matters, as with the chequer board, at other times it does not. All I am saying is that if you get this wrong you may mis-categorise an image.
So before going any further I would at least suggest that you create Category:Euclidean tilings‎ and canvass a proposal on how to handle higher dimensions.
— Cheers, Steelpillow (Talk) 16:13, 17 August 2013 (UTC)

• Created category Category:Euclidean tilings‎ by your suggestion. Subcategories also need to be renamed — maybe "Euclidean regular tilings", "Euclidean uniform tilings" and "Euclidean uniform dual tilings" would be better?
For other types of honeycombs or higher dimensions, probably there is no straightforward classification. The best I can suggest is to create separate category for each honeycomb with many (say, 5 or more) images. It is unlikely to harm in the future, and it could allow, for example, linking articles in Wikipedia and categories in Commons.
• Colorings are relevant only in context. In article, there are tables using images with additional information (grouping tiles etc.). But the image itself (without explanations) is just tiling, and it can be used in different contexts with different meanings. My point is that putting differently colored but otherwise identical tilings in the same place on Commons helps to locate them afterwards and does not really harm there (although of course there could be another category for e.g. checkered tilings). Maybe this should not be called classification of tilings but rather grouping images, while any proper classification (including higher dimensions and other classes of tilings) should rely on additional information provided by already existing articles in Wikipedia.
Stannic (talk) 21:11, 17 August 2013 (UTC)
Well, when I visited Category:Honeycomb images I was disappointed not to see any photographs of bees buzzing round their food stores. The current state is no basis for a robust and future-proof schema, it needs fixing from the ground up. Historically, terms such as "tiling", "tessellation", "honeycomb" and "space filling" have all been used in this context, as well as in related contexts, sometimes interchangeably and sometimes with distinct and incompatible meanings. My own view is that while "honeycomb" is fine in a specialist context where we all know what it means, as a way to categorise specialist images on a general resource it is wholly inadequate. The bees take precedence. Category:Honeycomb images means the same to the general visitor as Category:Honeycombs and should either redirect to it or be abandoned. "Tessellation" is just a fancy word for "tiling" and for clarity we should stick with the plainer one. I would prefer to use say Category:space fillings, or maybe Category:Tilings of 3-space which extends in an obvious way to higher dimensions. Using "tiling" more or less throughout would mean that category names for "plane" tilings need to be explicit. For example we would still need one named either Category:Euclidean plane tilings or Category:Tilings of the Euclidean plane. I regard this as a small price to pay for a correct, robust and extensible naming convention.
Colourings are really a matter of labelling the individual images so I will not worry about them further.
But I would like to add a big "Thank You" to you for having a crack at this. I have been too "busy" (a euphemism for faint-hearted) to do so myself. — Cheers, Steelpillow (Talk) 12:10, 18 August 2013 (UTC)
Tangent: I made the pix shown above, and tagged them as "equivalent". If consensus prefers another word, it can (sigh) be changed. —Tamfang (talk) 18:11, 19 August 2013 (UTC)

## Questions

• Assuming that the current top-level category Category:Tilings-db will remain as it is now, what should be most correct names for six its subcategories?
• For example, is it correct to use "Spherical plane tilings" or "Tilings of the sphere"? Maybe "Spherical polyhedra" needs to be merged with "Spherical tilings" under some name, considering that spherical polyhedron is tiling by definition?
• Also, you have pointed that Category:Dual uniform tilings‎ would more usually be phrased as Category:Uniform dual tilings‎ but I could not find sources where this is explained.
• For example, [1] and [2] seem to use wording "dual uniform polyhedra".
• Many images of hyperbolic tessellations here are named "File:Uniform dual ..." and no images are named "File:Dual uniform...".
• Article w:Uniform tilings in hyperbolic plane uses "dual uniform tiling" in text and "Uniform duals" in tables.
• Is there any difference? I was naming categories like "Dual uniform tiling V 4-4-4-5" (see here), and renaming could be done only if it is necessary.
• I just created Category:Tilings-db-temp to place some categories which are not in use now due to errors or changes but which could be probably used later (undecided). Also, any unidentified related images could be moved there.
• There are very many images of hyperbolic tilings here and here which need to be sorted. It would be too many for me, so they need to be sorted by others gradually.
• I really need opinions of other people involved in tilings and polyhedra regarding current system and naming. The categorization should be maintainable, and involved people need to know it.
• I will not probably made great changes for now and stick with current names (even if incorrect). Probably I'll collect scattered pictures of honeycombs in one category now.

Stannic (talk) 13:18, 18 August 2013 (UTC)

"Spherical polyhedra" has a good historical precedent and I would be happy with that. "Spherical plane tilings" is somewhat self-contradictory (ignoring plane projections of the sphere). "Spherical tilings" and "Tilings of the sphere" begin to run into ambiguities - there are spheres of many dimensionalities. "Tilings of the 2-sphere" is accurate and extends upwards but is less familiar than "Spherical polyhedra", so would be my second choice.
"Uniform dual" is more grammatical - these are duals of the uniform figures (as opposed to other figures), not uniform variants of dual figures. It is also the usual phrase found in academic references, along with "Archimedean dual" for polyhedra (used by both Cundy & Rollett and Wenninger, for example). I can provide fuller academic referencing if need be. Meanwhile your web links are to self-published sites, one by a non-native English speaker who even uses incorrect words like "polyhedras". And one's fellow wiki editors are hardly a reliably-sourced bunch.
And of course not forgetting higher dimensionalities.
So I would suggest the following top-level categories:
By degree of symmetry
By topological curvature
By dimensionality
Under these can come the sub-categories holding the actual images, for example:
... and so on
Yes, opinions from more editors would be good. We should at least wait a few days, and try to think of somewhere else to post notices. Meanwhile I am not sure that even minor changes which may have to be undone are worth getting on with, but I guess you can be the judge of that. — Cheers, Steelpillow (Talk) 17:46, 18 August 2013 (UTC)
— Cheers, Steelpillow (Talk) 17:46, 18 August 2013 (UTC)
To Steelpillow: I've checked references you have mentioned and agree with "Uniform dual" instead of "Dual uniform"; see proposed system below.
To User:Stannic, I've been watching the additions of Commonscat links for tiling article images, named by en:vertex configurations and looks good. But clear-thinking on categories is beyond me at the moment. But I'd not call it "-db" for database, at least when I hear that I think of the templates used for polyhedra and tiling stat tables. It seems better to just say Category:Tilings for 2D tessellations, and subcats Category:Spherical tilings, Category:Euclidean tilings, Category:Hyperbolic tilings. Then Honeycomb is often used for tessellations 3D or higher, and there's not many images above 3D! Tomruen (talk) 20:48, 18 August 2013 (UTC)
@Tomruen, do you have a proposal on how we can disambiguate "honeycomb" from the storage system used by bees? — Cheers, Steelpillow (Talk) 09:31, 19 August 2013 (UTC)
To Tomruen: As for changing Tilings-db to something else: currently there are three categories — Category:Tiles, Category:Tiling, and Category:Tessellations. These three categories are looped: ${\displaystyle Tessellations\subset Tiling\subset Tiles\subset Tessellations}$. Something is wrong there and probably requires analysis. I'm not sure how to deal with this.
Centralized category system for images of tilings really requires its own appropriate name and place. Otherwise it will become part of general mess.
I would suggest, after fixing names of subcategories (see below), to place Category:Tilings-db in Category:Polytopes and maybe rename it into "Tilings (geometry)" to disambiguate it from arbitrary decorative and natural tilings.
Stannic (talk) 17:11, 19 August 2013 (UTC)
Some further thoughts on the proposal and discussion to date:
— Cheers, Steelpillow (Talk) 20:24, 19 August 2013 (UTC)
• Added your suggestions as PLA and PSH (if I understood correctly, you suggest to separate all 2-dimensional tilings to spherical and not spherical)
• We will have two categories named Category:Tiling and Category:Tilings?
• Yes, there is not many 4d images; added as D-N (see below for all these codes)
• Added summary below, hope it will help.
Stannic (talk) 06:53, 20 August 2013 (UTC)
Ratusz w Słupsku - I piętro - kafelki IMG 0090 1600x1067 1600x1067
• Yes, there need not be a category for all 2-dimensional tilings. Category:Plane tilings would contain little more than the sub-categories for Euclidean, hyperbolic and projective plane tilings (and tilings of things like the affine, inversive and other obscure planes if occasion demanded), while Category:Spherical tilings is in this sense its own sub-category.
• Yes, probably. "Tiling" is the art of placing physical tiles on a substrate and getting your hands dirty, while "Tilings" are the mathematical patterns created. I say probably because whether "Tiling" remains a separate category from "Tiles" does not concern me.
• Also, in your proposed list below the "Tilings of 4-space" and "Regular tilings of Euclidean 4-space" could merge into "Tilings in 4 or more dimensions".
— Cheers, Steelpillow (Talk) 10:14, 20 August 2013 (UTC)
• One more: DUA is likely over time to grow related categories, for example quasiregular, semiregular, convex and non-convex duals, and so on. Not all of these will be uniform duals, and in this wider context the idea of one figure as the original and another as its dual shadow loses value - duality is a relationship between equals. One cannot predict the future but it would help to make allowances. So I'd prefer to see something like UND rather than DUA — Cheers, Steelpillow (Talk) 12:41, 20 August 2013 (UTC)

• DUA and others are just codes I've decided to use in this discussion, they will not be part of system. I can change this one as you suggest; I just feared that UND will be similar to UNI visually.
• I would still insist on making geometric component clear in the category name in some way. Using just "Tilings" will not separate it from all sorts of tiles and mosaics, including bee's storage systems, ceramic tiles and very beautiful but absolutely uncomputable geometrically tilings (example on the right). I could propose Category:Tilings (geometry) or Category:Tilings in geometry, or something like this. — Stannic (talk) 12:48, 20 August 2013 (UTC)
Apologies for my confusion over DUA. Now I understand, it's not a problem. But I disagree strongly about the need to separate mathematical tilings from real ones. For example hundreds of years ago at least one Islamic architect discovered quasiperiodic tilings and decorated a mosque accordingly. Any image of this work is at the very least of historical, mathematical and artistic importance. Or, what if someone takes a photograph of a medieval floor tiling and draws a mathematical diagram over the top of it? Or, to put it another way, do you know of any real tilings that are not geometric - apart from figurative mosaics as in (suggested by?) the image above? I don't believe we want tilings separated in the way you suggest, we want them all in the same place. Disambiguation links at the top of Category:Tiling and Category:Tilings should quickly resolve any confusion for the visitor. — Cheers, Steelpillow (Talk) 18:27, 20 August 2013 (UTC)

I see your point and I'm sorry for any confusion. It is true that tilings in geometry and real-world mosaics are connected in the history, and I totally agree with it. No need (and impossible) to separate real-world mosaics from mathematical tilings. Even opposite, the same image can belong (in common sense and technically here) to many categories.
What I was trying to say is that, we are thinking of appropriate name for what is currently called Category:Tilings-db. Tilings-db is an attempt to categorize tilings (both abstract and real-world when it is possible) by mathematical structure - regular, uniform etc. If we are going to use special separate category for this system, then I believe that simple name "Tilings" would be misleading for it: tilings are not primarily mathematical tilings, visitor will not expect to see some classification like this one in category named "Tilings". Of categories I've seen, more "general" is Category:Tiles, this one includes history, art, etc. Category Tessellations, on other hand, contains many mathematically-named subdirectories although names "Tiles" and "Tessellations" do not suggest that second would be more math-related (as you said before, "tessellation" is just a fancy word for "tiling").
Or we could place categories like Uniform dual tilings of Euclidean 3-space (and all level-1 categories below) directly in Category:Tessellations; it is on-topic there but Category:Tessellations is already filled with various mathematical aspects of tilings, so I believe it makes sense to create separate category which I hastily named Category:Tilings-db.
Maybe my suggestion to rename Category:Tilings-db to "Tilings (geometry)" was misleading. It could be named, for example, "Tilings by geometric properties".
Also, I've simply emptied category "Tiling" (which was one of three in the loop) because it was containing the same kind of images as Category:Tiles, two categories filled with content related to ceramic or stone tiles ad tiling process (I've placed them under Category:Tiles), and several categories fitting with current content of Category:Tessellations (I've placed them there). It is not to separate geometry and real world, it is because two categories Category:Tiles and Category:Tessellations cover what was in "Tiling", and no need for another category with just some arbitrary content from two categories without clear distinction why this content was selected.
Sorry for any misunderstanding. Stannic (talk) 20:01, 20 August 2013 (UTC)
To be accurate, "Tiles" are the modular objects themselves, "Tiling" or "Tessellation" (verb) is the act of assembling tiles or (noun) a single resulting pattern, "Tilings" or "Tessellations" are the resulting patterns, and a "Mosaic" is an irregular design in which the overall artistic image rather than the tile or "tessera" shape dictates the design, and is usually understood as a distinct art form from tiling. Real-world mosaics are not mathematical tilings, but real-world tilings are. I think that some of your recent changes are not consistent with this. For example things like grout, adhesive, history and so on should most certainly have stayed in Category:Tiling. Then, if need be, Category:Tiles can become a sub-category of that just for the tiles themselves. And Category:Tessellations does need to change to the more common word, Category:Tilings. So I see what you mean about not using that for your database. How about using Category:Geometric tilings ? — Cheers, Steelpillow (Talk) 14:54, 21 August 2013 (UTC)

┌─────────────────────────────────┘

• If we are going to rename Tessellations to Tilings in Commons, then we are going also to rename w:Tessellation to w:Tiling to be consistent. w:Tiling is currently disambig. After looking at this disambig, not sure about changing Tessellations to Tilings now.
One could discuss need for renaming w:Tessellation to w:Tiling on w:Talk:Tessellation (and renaming Category:Tessellations as you suggest) where it will get more attention.
It is impossible to do all at once, and Tessellations is rather extensive category. My feeling is that better to let it remain Tessellations, at least for now, given that it is just another synonym for tiling.

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

• Renaming Tilings-db to Geometric tilings would also suggest idea of separating tilings to geometric and non-geometric, as with variants Tilings (geometry) or Tilings in geometry. Given that real-world tilings are geometric tilings, and tilings and tessellations are synonyms, this is equivalent to putting subcategories of Category:Tilings-db to Category:Tessellations and getting rid of Category:Tilings-db at all.
After some thought, it is not that bad. It is possible to place ordered categorization by geometric properties separately, as it was done here with polygons (they are categorized there by the number of sides in main category, instead of creating special subcategory named "Polygons by number of sides").
I would agree with moving content of Category:Tilings-db to main category Category:Tessellations ordered in appropriate way, after it will be finished.
Renaming Tilings-db to Tilings by geometric properties, on the other hand, would emphasize that subcategories of it are, well, geometric properties: dimensionality, curvature, regularity, periodicity, the number of symmetries, something else.
• How you would suggest to categorize Category:Tiling, given that things like grout, adhesive, history and so on will be in it, and given that Category:Tiles will become a sub-category of that just for the tiles themselves? Where to place it — under Category:Flooring and somewhere else?

Stannic (talk) 18:02, 21 August 2013 (UTC)

What title suits an image category and what name suits an encyclopedia article are different issues, and anyway Wikipedia has got in a mess over these things too, don't use that as your guide. If we force complete consistency between the two sites then both will be broken. Do you want to fix Wikipedia before going further here?
We also have to bear in mind that, although we are here interested in mathematical classification, both the Commons and Wikipedia are concerned with every aspect of tiling: a name that makes sense to a mathematician may need disambiguating or qualifying in the wider context of the whole site. And where a category name addresses both the wider and the mathematical nature of images, it needs to be sensible in the wider context without needing disambiguation.
Category:Tessellations already has lots of geometrical "tiling" categories in it. It might be a very good idea to start by putting all our main categories into the same one, which I still believe very strongly should be called Category:Tilings and not Tessellations. If they do not order sensibly in there with all the others, then we can always create a new Category:Tilings (Geometry) or whatever.
Category:Tiling could be made a subcategory of Tiles (if that is kept), Flooring, Decorated walls, Wall textures, Categories partly containing textures, Construction, and probably a good few others.
• Some subcategories of Category:Tessellations could be inserted — gradually — in the so-called "database". For example, "Aperiodic sets of tiles" and "Aperiodic tiles" could be inserted as "Non-periodic tilings of the Euclidean plane" (almost all images there are Euclidean 2D). But such things as "Tangrams", "Squaring the square" or, for example, "Penrose tilings" in my opinion must remain as immediate subcategories of Category:Tessellations. While I agree that Category:Tessellations is slightly over-crowded, I also agree that Commons and Wikipedia are concerned with every aspect of tiling. And we anyway cannot simply decide here what aspects are/more interesting and what aren't/less.
• If I understood correctly your last reply, you would agree with merging Category:Tilings-db into Category:Tessellations, but insist on renaming before Category:Tessellations to Category:Tilings. While I can agree that name "Tilings" is better than name "Tessellations" in this case and may need to be used instead,
1. I do not believe that putting it all (current content of Tessellations, unfinished content of Tilings-db and new categories of Tilings-db) in one large heap now is a good idea;
2. Renaming Category:Tessellations to Category:Tilings will involve creating yet another category, moving all the content, description, fixing links etc.;
3. Probably two people is too small number in this case to make sure we are not doing something wrong.
So we could do the following:
1. Discuss now any existing inconsistencies in the currently proposed below structure of "database" and naming its subcategories;
2. After discussing and fixing any problems, create category structure in the category Category:Tilings-db (as proposed below in the next section) and order all unsorted files (not including lots of unsorted hyperbolic tilings which will need days of careful sorting by vertex/face configuration);
3. After creating mentioned two-level structure, think again how to deal with Category:Tessellations; maybe there will be other replies and ideas here by that time. Note that we are going to have just a few level-1 subcategories in Category:Tilings-db after all (10 or so), so moving them into the right place later will not be problem anyways. One can think of Category:Tilings-db as temporary now.
In short, I strongly believe that it is better to do it sequentially, rather than in parallel, and placing them all together will not help. Please state whether you agree with this.
Stannic (talk) 21:39, 21 August 2013 (UTC)
I think we understand each other much better now and I agree with most of what you say. Yes, it is better to do things one step at a time, as you ask me. We may make mistakes but that will still be better than the present mess. And yes, more people would help. Also to rename Tessellations to Tilings is a big move and probably controversial, so we would need to follow Commons:Rename a category and advertise a discussion more widely. That discussion might also draw in more helpers, so we could start it while the other changes are being made, and only rename Tessellations later. On a point of detail, aperiodic tiles in higher than 2 dimensions do exist, such as the Schmitt-Conway biprism. So please always be careful not to put a general category such as "Aperiodic tilings" under a two-dimensional category such as "Non-periodic tilings of the Euclidean plane", even if it currently contains only 2-D tilings.
Did I change my mind over Tiles and Tiling? I must apologise then, but it does not matter to me. I have said that I am only concerned with the mathematical categorisation, and I have not thought deeply about the other aspects. You may take my muddled opinion on grouting as you find it, I will not mind.
— Cheers, Steelpillow (Talk) 09:40, 22 August 2013 (UTC)
Nominated Category:Tessellations for discussion; see Commons:Categories for discussion/2013/08/Category:Tessellations. — Stannic (talk) 12:14, 22 August 2013 (UTC)

## Proposed system

This is the proposed (not implemented yet) system to be discussed. Feel free to change anything incorrect or misleading in this section and/or suggest changes.

Stannic (talk) 16:12, 19 August 2013 (UTC)

## Category:Uniform tilings of Euclidean 3-space

• Created this category to collect honeycombs as this name agrees with "Uniform tilings of 3-space" by Branko Grunbaum. If there are no objections against proposed names of second-level categories (see "Proposed system" section above), then I'll start create these too tomorrow or day after.

Stannic (talk) 11:22, 21 August 2013 (UTC)

Stannic (talk) 11:45, 26 August 2013 (UTC)

## Schlegel diagrams and vertex figures

Alternated order-5 cubic honeycomb verf
Order-3 icosahedral honeycomb verf
Cubic honeycomb verf
• Will it be correct to name category for these images "Tilings of 3-space (vertex figures)" and put it under Tilings of 3-space? Or "Tilings of 3-space (vertex figures as Schlegel diagrams)" will be better? — Stannic (talk) 17:58, 26 August 2013 (UTC)
A Schlegel diagram and a vertex figure are very different things. One can create a Schlegel diagram of the vertex figure of a higher polytope (which is what tilings of 3-space are), but it is not the vertex figure, just a Schlegel diagram of the vertex figure. So I would suggest using "Tilings of 3-space (Schlegel diagrams of vertex figures)" and place it in "Tilings of 3-space (vertex figures)". There is a Category:Schlegel diagrams that it can also be placed in, and there ought to be a Category:Vertex figures that "Tilings of 3-space (vertex figures)" can also be placed in. Does that make sense? — Cheers, Steelpillow (Talk) 20:52, 26 August 2013 (UTC)
OK, I created Category:Vertex figures. It may need a little editing? — Cheers, Steelpillow (Talk) 21:01, 26 August 2013 (UTC)
Thanks, just created Category:Tilings of 3-space (Schlegel diagrams of vertex figures). Did not create Category:Tilings of 3-space (vertex figures), it can be created if/when necessary. — Stannic (talk) 21:35, 26 August 2013 (UTC)

## 999 and 3.4.3.4.3.4

Does 3.4.3.4.3.4 count as quasiregular tiling, or quasiregular tilings are only those with four faces around vertex? Definition in article w:Quasiregular polyhedron is that it does, but I'm just unsure and asking here to clarify. — Stannic (talk) 21:10, 28 August 2013 (UTC)

There are ambiguities and inconsistencies in the published sources that I know about. I am not aware that the idea of sixfold vertices has even been discussed in the context of quasiregularity. They meet some definitions of quasiregularity seen elsewhere but not others. My own view is that they are quasiregular, it just needs someone reliable to stand up and say so. Perhaps such a source already exists and I have not seen it. But until someone here or on say Wikipedia does reference it, we must avoid original research and treat them as not quasiregular. I have asked the question at w:Talk:Quasiregular polyhedron#Sixfold vertices (Wikipedia) — Cheers, Steelpillow (Talk) 11:30, 29 August 2013 (UTC)

## Proposal to move images of hyperbolic tilings

Currently there are 999 images of hyperbolic tilings in categories Poincaré Disc and Hyperbolic tilings (each image is categorized under both of these).

The proposal is to include all them to the category (created by me) Category:Unidentified tilings, and exclude them from categories Poincaré Disc and Hyperbolic tilings. This would allow releasing category Poincaré Disc for arbitrary drawings on this model, and this would clean category Hyperbolic tilings which is in the substructure of Category:Tilings-db.

Are there any objections against this large move? I just made trial-trip with Cat-a-lot (moved five images there and back again), so I believe it would do what is needed, but I'll wait for comments on this post. — Stannic (talk) 17:01, 29 August 2013 (UTC)

I can't say I understand the plan. Will each tiling be moved back to the same categories once it's identified, or are you making a new category for uniform tilings in the P-disc? —Tamfang (talk) 17:41, 29 August 2013 (UTC)
Aren't they all (almost) in the P-disc? (Some counterexamples are here: order-3 heptagonal tilings in half-plane and on Klein's disc).
The images will be later moved in subcategories of Category:Hyperbolic tilings. I am not currently distingushing models since there are so few images not on P-disc. — Stannic (talk) 18:03, 29 August 2013 (UTC)
There are other representations of hyperbolic tilings, besides the Poincaré disc. Ideally we should have sub-categories of Hyperbolic tilings, say Category:Tilings of the Poincaré disk, Category:Tilings of the Beltrami-Klein disk and Category:Tilings of the Poincaré half-plane. These should all be crossed with the sub-categories for Regular, Uniform and Uniform dual tilings of the hyperbolic plane‎ to give nine sub-sub-categories along the lines of "Regular tilings of the Poincaré disk" and so on. The images can then be moved into these bottom-level categories and deleted from Poincaré Disc and Hyperbolic tilings. However I can understand if you want to do things a simpler way. (A word of caution: The two disk models can look quite similar. Care needs to be taken that the correct projection has been identified.) — Cheers, Steelpillow (Talk) 19:04, 29 August 2013 (UTC)
Well, I'm aware about existence of other representations.
If need be (e.g., if some day there will be 999 pictures of tiling {7,3}, and 333 of them will be on half-plane model, 333 on Poincaré Disc and 333 on Beltrami-Klein disk), then one could create three subcats there named "Order-3 heptagonal tiling (<name of model>)".
One could suggest also using top-level cats named "Tilings of the <name of model>", second-level cats named "<degree of regularity> tilings of the <name of model>" etc. and cross them all using w:Cartesian product, but imo it is unlikely to be useful: it is harder to maintain, and you’ll be spoilt for choice when you come to Tilings-db.
One possible counter-argument/objection is that someone incoming could search for hyperbolic tilings on Poincare disk in Poincaré Disc but will not find them, so the system isn't ideal. However, it is possible to place in category Poincaré Disc the following or similar line:
See also category Hyperbolic tilings for hyperbolic tilings, including tilings on Poincaré Disc model.
The system will still not be ideal but it will never be anyway.
And thanks for caution, I'll try my best at recognizing them. — Stannic (talk) 20:01, 29 August 2013 (UTC)
Yes the sub-sub-categories are a pain to maintain but we need only do it when there are enough images for it to be worth doing. For just a few images we can put them all in a single higher-level category. But if we are categorising many images by both <model> and <regularity> then finer-grained categorisation will become inevitable. — Cheers, Steelpillow (Talk) 12:02, 30 August 2013 (UTC)
The issue of searching for the Poincaré Disc is easy to solve. Just add the code [[Category:Poincaré Disc]] to Category:Tilings of the Poincaré Disc (or whatever you all it) and it will appear in Poincaré Disc in the section above the image gallery, just where it is needed. — Cheers, Steelpillow (Talk) 12:02, 30 August 2013 (UTC)
There are a small number of non-disk-Poincare images, half-plane one at Heptagonal_tiling, and Klein projection at Triheptagonal_tiling, hmmm... maybe only 2?! I have a special version of KaliedoTile from Jeff Weeks that can draw Klein-disk models, if we need more, although more work per image than Anton's batch output! Tomruen (talk) 21:00, 29 August 2013 (UTC)
Hyperbolic domains klein 753
So I've checked images in Category:Hyperbolic fundamental domains and should say I was quite wrong about small number of images on Klein disc; there are ~100 (IICC, 99?) images on Klein disc in that category. But for some reason these Klein-disc images are also included in category Category:Poincaré Disc. One example is on the right.
Yes, vast majority is in P-disc (over 1000 in total, including regular, uniform and uniform dual tilings). Several dozens are in Beltrami-Klein disk, and most of them are uniform duals (few images of uniform tilings also). Have seen only two or three images of regular tilings in half-plane projection. My personal choice would be for new images on half-plane model, just because it looks quite differently and could be useful in articles to show the same thing in two ways, but disclaimer: I do not know at all how it is hard technically/if it is feasible to create images on half-plane, and I do not know what is really needed for articles about tilings.
My feeling is that for any particular tiling (e.g., snub tetrapentagonal tiling), there will be at most few dozens of images in total, including three projections, different colorings and all that. (For this reason, I am currently putting uniform and corresponding uniform dual tilings in the same place). Maybe even there is no need for more images on the same projection (although it could be better to have choice). Am I wrong about this all? — Stannic (talk) 15:59, 30 August 2013 (UTC)
First, if I were you I would not move anything until the final categories have been decided. Otherwise they will end up being moved repeatedly, which is a waste of time. Nor would I worry about generating half-plane projections or what articles need, at least not here. Just focus on the Categories - one thing at a time! Once all the images are in the right places, it will be much easier to see what is missing. — Cheers, Steelpillow (Talk) 16:54, 30 August 2013 (UTC)

## Categories for uniform dual hyperbolic plane tilings

For uniform tilings, there are categories named "Uniform tilings of the hyperbolic plane with <name of regular polygon>s", e.g. Category:Uniform tilings of the hyperbolic plane with heptagons.

If uniform tiling has heptagonal faces, then its dual has seven-fold vertices, and vice versa. More generally, if uniform tiling has k-gonal faces, then its dual has k-fold vertices, and vice versa. If uniform tiling has apeirogonal faces, then its dual has ideal vertices. So categories for uniform dual tilings could be named like Category:Uniform dual tilings of the hyperbolic plane with 7-fold vertices or Category:Uniform dual tilings of the hyperbolic plane with ideal vertices. Pairs of "dual" categories (e.g. Category:Uniform tilings of the hyperbolic plane with heptagons and Category:Uniform dual tilings of the hyperbolic plane with 7-fold vertices) could be interlinked horizontally.

Any improvements or objections? — Stannic (talk) 18:46, 30 August 2013 (UTC)

Looks good to me. — Cheers, Steelpillow (Talk) 19:57, 30 August 2013 (UTC)