Talk:Tessellations by Recognizable Figures
The table of symmetry types I-X bugs me. It's Escher's own work, translated by (or for Doris S.), so we maybe should mention that.
But more troublesome is, as you point out, what these things mean is not exactly clear. I'd be content to just give the symmetry group correspondance, or maybe discuss in our own words. I never teach this stuff - I just do the ones later on the page and really only point out Escher's categorization because it's about him.
I've thought about the swans sketch a bit, and I know what he means - I wrote it up in the text. But my feeling is, the table and Escher's personal view of glide reflection symmetry is better avoided.
Bryan 00:35, 18 May 2007 (CDT)
Where did these graphics come from with grey/white patterns with hooks? Did you create them or find them somewhere?
Bryan 00:49, 18 May 2007 (CDT)
The grey-white patterns were done by me. I copied them after Escher's own sketches, but I organized them a bit different.
The rotation about a vertex section is problematic. Escher never does anything quite like that, and it's because you only get to change one edge of the square and it has four uses. His Type X are far more flexible. On top of that, looking at a sketch like the classic Sketch #35 (Lizards) shows that doing it with hexagons has a lot more flexibility as well. I'd fix it, but it's late and easier to just note the shortcomings for now.