I'd be surprised if the pinwheel tilings — which have tiles that take on an infinite number of relative angles — could be reproduced in this manner. It seems li

I'd be surprised if the pinwheel tilings — which have tiles that take on an infinite number of relative angles — could be reproduced in this manner. It seems like projecting a periodic set in high dimensions should give at most a finite number of cell orientations, although I can't prove it offhand.