There is a lattice consisting of three sets of lines, all at 120 degrees to each other. Unlike a lattice of equilateral triangles, the lines are shifted a little so that they only intersect two at a time. The result is a plane tessellated with hexagons and triangles- it looks a bit like lots of Stars of David. Does anyone know the name of this lattice? I thought it was called the “kogome lattice,” but I can’t find anything on google under that name. I do know that it has a Japanese name, because it’s named after a Japanese word for straw mats.
It’s spelled “Kagome.” It means “basket pattern” in Japanese. Straw mats have a very different pattern (mostly parallel lines with some lines at a 90-degree angle).
A bit of trivia which is probably completely useless to you: It’s impossible to place a square (of any size) on a Kagome Lattice such that the four corners of the square rest on lattice points. Cool, huh?
Thanks for the info, guys- I guess there’s a good reason why “tatami lattice” didn’t get me anywhere. Can you suggest a good book with info on the Kagome lattice? I checked the geometry junkyard, but without a lot of luck.