Talk:Tiling

message: need to mention Roger Penrose's work on tilings
This has been done a while ago, see tiling page. Karlscherer3 01:35, 19 Jun 2005 (UTC)

message: this article is quite meandering and off. The main issues are not discussed:
* definition of a tiling.
* definition of vertexs, edges, and tiles.
* k-hedral. A tiling is k-hedral if it has k prototiles.
* k-gonal. A tiling is k-gonal if it has k types of vertices.
* k-toxal. A tiling is k-toxal if it has k types of edges.
* consider the number of types of tiles, vertices, edges, with respect to the tiling's symmetry, we have k-isogonal, k-isohedral, k-isotoxal tilings. That is, if the symmetry of the tiling maps the prototiles into k classes, then that tiling is k-isohedral.
* definition of regular tilings.
* definition of archimedean tilings.
* the problem of a tiling of r prototiles admits m number of tilings. If r==m==1, it the prototile is said to be isomorphic. If r==m, it's r-morphic.
* topological class of tilings.
* duality
* aperiodic tilings.
Xah Lee 02:53, 2004 Sep 1 (UTC)
Good suggestions, so why didn't you add them in?
I will add your suggestions, but maybe you can help edit the tiling page, because you seem very knowledgable in this area. Any help is welcome and more constructive than suggestions. By the way, aperiodic tilings have their own page, and the link is there. Karlscherer3 00:25, 19 Jun 2005 (UTC)
thread_title: article meandering and off

message: What is the difference between tiling and tessellation? --Henrygb 00:36, 25 Mar 2005 (UTC)
thread_title: Tessellation

message: There exists an article on Wallpaper groups. The tiling article and Wallpaper groups should mention each other. Dmharvey 19:35, 30 May 2005 (UTC)
thread_title:  wallpaper groups 

message: The article says examples of all 17 wallpaper groups can be found at the Alhambra. Does this rely on coloring to break a higher geometric symmetry? Can we confirm this with photographs?
B. Grünbaum, and later B. Grünbaum, Z. Grünbaum, & G. C. Shephard, assert that p2 and p3m1 are not found at the Alhambra, but do appear nearby in Toleda from about the same period; however pg and pgg are completely missing from Islamic art of the time. Contradicting this is an article by R. Pérez-Gómez entitled "The four regular mosaics missing in The Alhambra", asserting that the missing groups are not missing.
Not having copies of these articles, nor photographs to support the claim of 17, unlike the claim of 13, I'd like to see something definitive.
Anyone? KSmrq 21:38, 10 Jun 2005 (UTC)
thread_title:  Alhambra symmetries 

message: With regard to the notice about "abnormal terminology", I think the proper source for choosing preferred terminology would be Grünbaum and Shephard, Tilings and Patterns, which still serves as the standard work in the area although largely written in the 1970s.  For example, "Neat tilings" should be "edge-to-edge", "Nowhere-neat tilings" should probably be "unilateral", "Polysquares" should be "Polyominoes" without mention of the nonstandard term "Polysquares" (there is no tiling content in that section at present, but tiling with polyominoes is a legitimate topic to discuss here), "Pure tilings" should be "monohedral", and concepts described in the article which are not discussed in Tilings and Patterns may not be important enough to cover unless referenced to multiple articles reviewed in Math Reviews. Joseph Myers 19:09, 23 Jun 2005 (UTC)
thread_title:  Terminology