Talk:List of convex uniform tilings

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too technical tag[edit]

i removed the tag. the article has undergone many edits since the tag was added. if you feel the tag still belongs, feel free to add it back but please leave some specific suggestions about what you think the article is missing. thanks. Lunch 04:56, 24 September 2006 (UTC)

39 uniform tilings[edit]

I have expanded the nonconvex tiling section to a complete list from Coxeter. I'll try to get some images and better tables going in the near future.

I'm thinking to combine all 39 into one table, if it makes sense when I have images for all of them.

Tom Ruen 13:58, 14 January 2007 (UTC)

The list of tilings with apeirogons in Uniform Polyhedra is not complete. A more complete list is in Grünbaum, Miller and Shephard, Uniform Tilings with Hollow Tiles, pp 17-64 of The Geometric Vein: The Coxeter Festschrift. To quote p.57, "Since 1953 several new tilings using apeirogons have been discovered". This also considers tilings using zigzags, which also meet the flag-transitivity condition for being considered infinite regular polygons. I don't know if more have been found since 1981 or if completeness has been proved. Joseph Myers 00:55, 22 January 2007 (UTC)


This article is way to large! It takes over ten minutes to download it by dial-up connection. —Preceding unsigned comment added by (talk) 20:22, 8 September 2007 (UTC)

Tilings in hyperbolic plane - which representation?[edit]

The introduction to this section says Shown with Poincaré disk model. In the Poincaré model, lines of the geometry are segments of circles contained in the disk orthogonal to the boundary of the disk, or else diameters of the disk. Some of the figures shown here, for example Order-4_pentagonal_tiling, use Euclidean straight lines to represent lines of the geometry and so appear to be shown with the Klein model. Nick Levine 18:01, 3 November 2007 (UTC)

The lines do look straight. I'm not sure if they are actually drawn straight, or just look that way, but the projection is Poincaré disk model. The Klein model looks very different - polygons get flattened near the boundary. Tom Ruen 18:52, 3 November 2007 (UTC)
Yeah, I agree, it does look like the Poincaré projection. But the lines look wrong, in some cases clearly so. Hmm, that's going to be an annoying job to fix. Nick Levine 19:11, 3 November 2007 (UTC)
Okay, I uploaded a new version with curved edges Image:Uniform tiling 54-t0.png - it was a checkbox in the program. I don't have the time to remake them all that way if you really like it better. It's just a difference between drawing lines on the hyperbolic plane, or drawing lines in the projected disc. I thought the topology was the important thing. Tom Ruen 21:50, 3 November 2007 (UTC)
Thanks. For the avoidance of future doubt, should we than note at the head of the section what's going on? Nick Levine 20:05, 4 November 2007 (UTC)

What software are you using to generate the images?[edit]

I am currently working with Louis Romero on a tiling software package and would like to avoid re-inventing the wheel.


Kenneth Ryan (intier at sourceforge) —Preceding unsigned comment added by (talk) 22:04, 29 June 2008 (UTC)

I used free software, Kaleido Tile, for some of them [1]. Tom Ruen (talk) 03:24, 30 June 2008 (UTC)

Topologically equivalent??[edit]

Are any tilings in this article topologically equivalent to:

Take the familiar square tiling. Divide one square into 2 equal parts by a vertical line. Have each row and column alternate between vertically-divided squares and horizontally-divided squares. (Squares that meet at a corner will always be divided the same way.) Georgia guy (talk) 15:31, 25 February 2011 (UTC)

For clarification, I mean to take the image on the lower left corner of:

Square tiling uniform colorings.png

and cut all red squares horizontally and all yellow squares vertically. Georgia guy (talk) 15:35, 25 February 2011 (UTC)

This? Cairo_pentagonal_tiling#Related_polyhedra_and_tilings Tom Ruen (talk) 19:25, 25 February 2011 (UTC)