Tessellation - Tessellations and Color

Tessellations and Color

When discussing a tiling that is displayed in colors, to avoid ambiguity one needs to specify whether the colors are part of the tiling or just part of its illustration. See also symmetry.

The four color theorem states that for every tessellation of a normal Euclidean plane, with a set of four available colors, each tile can be colored in one color such that no tiles of equal color meet at a curve of positive length. Note that the coloring guaranteed by the four-color theorem will not in general respect the symmetries of the tessellation. To produce a coloring which does, as many as seven colors may be needed, as in the picture at right.