A coloring of a plane tessellation (or indeed of any planar
graph) is a labeling (by "colors") of the tiles (i.e. regions) of the
tessellation in such a way that no two tiles which share an edge have the
same color. A coloring is perfect if every isometry of the tessellation
permutes the colors. For example, the ordinary black-white coloring of the
regular tessellation (4,4,4,4) ("chessboard") is a perfect coloring. If
every vertex of the tessellation has the same degree, say Some of the perfect colorings of the eight Archimedean tessellations of the Euclidean plane are also precise. The purpose of this note is to illustrate all of these precise perfect colorings, as well as those precise colorings which are only chirally perfect. |