User:Stannic/Categories for tilings

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

• 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

  • Regular tilings
  • Uniform tilings
  • Uniform dual tilings

  Group 3 — by dimensionality

  • 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 — 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 — 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 — 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.

Navigational templates

• 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

• 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}