Newsgroups:sci.mathFrom:mark@oracorp.com (Mark Bickford)Subject:3-color the Penrose tiling?Organization:Odyssey Research Associates, Inc.Date:Tue, 24 Aug 1993 18:26:40 GMT

Does anyone know whether the Penrose tiling is 3-colorable? Note: This question makes sense because a graph is 3-colorable iff every finite subgraph is 3-colorable, and any two Penrose tilings have the same finite subgraphs. When playing with some colored Penrose tiles, I never got stuck when using only three colors (until I ran out of tiles of those colors!), but no criteria that I could find that imply three colorabilty seem to apply to the Penrose tiling. I also couldn't come up with a general method to 3-color the dilation of a three colored (finite) tiling. ---Mark Bickford