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(some notes for collaborative study)

2 chapters from Martin Gardner's book "Penrose Tiles to Trapdoor Ciphers"

is this still unproven? ->

A Penrose tiling can, of course, always be colored with four colors so
that no two tiles of the same color share a common edge.  Can it always be
colored with three? It can be shown, Conway said, from the local isomorphism
theorem, that if any Penrose tiling is three-colorable, all are, but so far
no one has proved that any infinite Penrose tiling is three-colorable.