Funny, I was just thinking about that Archimdean tiling the day before, since it's dual to the "Cairo" tiling by (non-regular) pentagons. In fact of all the Archimedean tilings of the plane, I find that one to be the least appealing, aesthetically. And I was asking myself why I have that reaction. I think it's because of two contradictory first impression of those squares and triangles is that they're chaotic. And the second impression is that with so many triangles arranged edge-to-edge, it looks unduly tame. On the other hand, the dual tiling is perhaps the most beautiful Archimedean dual. http://en.wikipedia.org/wiki/Cairo_pentagonal_tiling . << There's a pretty Archimedian tiling with vertex figure 3.3.4.3.4 . . .
Daniel Asimov Visiting Scholar Department of Mathematics University of California Berkeley, California