Newsgroups:     sci.math
From:  (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