Coxeter mentioned (I believe in the Rouse Ball book) that one would like to know the number of different tilings by rhombs of the regular 2n-gon. I never asked him whether he believed that it might be possible to find an expression valid for any n. (I imagine he had no such belief.) It doesn't take more than a moment to prove that (ignoring rotations and reflections) there are six tilings of the 10-gon, but doing the counting for the 12-gon is tedious. In 1995 I wrote a program called Ovalturn that scans the n connected strips ('ladders' is the informal name Branko Grunbaum suggested for them in 1979 or 1980) of n-1 rhombs between opposite boundary edges, and performs a halfturn rotation on every 'oval' (hexagon tiled by three rhombs) it encounters. After it has once traversed all n ladders (in cyclic order), it goes around again (etc.). I let this program run for a while on the 12-gon and printed out the tiling after every ovalturn. When I cut out the printouts of all these tilings and sorted them into piles, I found I had 49 different patterns. I believe I caught them all, but it would be nice to have a better way to do the counting! Alan Schoen