# User:Stannic/Categories for tilings

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The summary of category system for tilings (under construction).

- Root category is Category:Tilings-db.
- The main discussion is at Category_talk:Tilings-db. Please post any replies on that page.

## Current structure^{[1]}[edit]

- Categories on level 1:
- Group 1 — by geometry

- Euclidean tilings — for any tilings of Euclidean space in any number of dimensions
- Hyperbolic tilings — same for hyperbolic space
- Spherical tilings — same for tilings of
*n*-sphere (including spherical polyhedra when*n*= 2)

- Group 2 — by regularity

- Group 3 — by dimensionality
^{[2]}

- Plane tilings — tilings of Euclidean plane or hyperbolic plane
- Spherical polyhedra — tilings of 2-sphere
- Tilings of 3-space
- Tilings in 4 or more dimensions — for all higher-dimensional honeycombs

- Categories on level 2:
- Regular tilings of the Euclidean plane
- Uniform tilings of the Euclidean plane
- Uniform dual tilings of the Euclidean plane
- Regular tilings of the hyperbolic plane
- Uniform tilings of the hyperbolic plane
- Uniform dual tilings of the hyperbolic plane
- Regular spherical polyhedra
- Uniform spherical polyhedra
- Uniform dual spherical polyhedra
- Cubic honeycomb — essentially, it is Category:Regular tilings of Euclidean 3-space
- Uniform tilings of Euclidean 3-space
- Uniform tilings of hyperbolic 3-space
- Uniform polychora
- Tilings of 3-space (Schlegel diagrams of vertex figures) — Schlegel diagrams of vertex figures of tilings in Euclidean or hyperbolic 3-space.

- Categories below level 2:
- Order-5 square tiling
^{[3]}— an example of naming categories for**regular**2-dimensional tilings. Adjectives are*triangular*,*square*,*pentagonal*,*hexagonal*,*heptagonal*,*octagonal*,*nonagonal*,*decagonal*,*hendecagonal*,*dodecagonal*,*apeirogonal*. - Uniform tiling 3-3-4-3-4
^{[3]}— an example of naming categories for**uniform**2-dimensional tilings with two or ore types of faces. This particular category contains images of snub square tiling; the category is named by its vertex configuration (3.3.4.3.4). - Uniform dual tiling V 4-6-14
^{[3]}— an example of naming categories for**uniform dual**2-dimensional tilings. This particular category is intended for images of tiling with face configuration V 4.6.14 (order 3-7 kisrhombille). - Regular square tilings of the hyperbolic plane — category contains all categories "Order-k square tiling" plus category Infinite-order square tiling. Similar categories exist for triangles, pentagons etc.
- Uniform tilings of the hyperbolic plane with squares — category contains all categories "Uniform tiling ...-4-...". Similar categories exist for triangles, pentagons, hexagons etc.
- Uniform dual tilings of the hyperbolic plane with 4-fold vertices — category holds subcategories "Uniform dual tiling V ...-4-...". Similar categories exist for
*k*-fold vertices (*k*= 3...8,10,12,14,16) and ideal vertices.

- Order-5 square tiling

## [edit]

- Template:See regular spherical polyhedra — used at seven pages.
- Template:See regular tilings of the Euclidean plane — used at three pages.
- Template:See regular tilings of the hyperbolic plane — examples of usage are here and here.
- Template:See uniform tilings of the hyperbolic plane — an example of usage is here.

## To-do list[edit]

- Unsorted images.
~~Need to decide what is better — many dynamic templates, varying from category to category, or one static on all categories~~Create single navigational template (like this one). Links (draft):- L1: R, U, UD, E, H, ST, P, SP, 3D, ND, UI
- L2: ER, EU, EUD, HR, HU, HUD, SPR, SPU, SPUD, E3U, H3U
- R2: {3,6}{4,4}{6,3}; {3,3}{3,4}{3,5}{4,3}{5,3}; {2,n}{n,2}; {3,n}{4,n}{5,n}...
- U2: -3-4-5-...-16-
- R3: {4,3,4}

## Notes[edit]

- ↑ It is not known yet whether Category:Tilings-db will remain separate category or subcategories of it will be merged into Category:Tessellations. Currently level-1 categories are shown both under Category:Tilings-db and under Category:Tessellations. Besides, renaming Category:Tessellations to Category:Tilings is being discussed at CfD.
- ↑ 2-dimensional case is partitioned into two subsets: plane tilings and spherical polyhedra.
- ↑
^{a}^{b}^{c}Both in "Order-5" and in "3-3-4-3-4" is used hyphen-minus (minus from numeric keypad).