In geometry, a uniform coloring is a property of a uniform figure (uniform tiling or uniform polyhedron) that is colored to be vertex-transitive. Different symmetries can be expressed on the same geometric figure with the faces following different uniform color patterns. A uniform coloring can be specified by listing the different colors with indices around a vertex figure.
n-uniform figures In addition, an n-uniform coloring is a property of a uniform figure which has n types vertex figure, that are collectively vertex transitive.
Archimedean coloring A related term is Archimedean color requires one vertex figure coloring repeated in a periodic arrangement. A more general term are k-Archimedean colorings which count k distinctly colored vertex figures. For example, this Archimedean coloring (left) of a triangular tiling has two colors, but requires 4 unique colors by symmetry positions and become a 2-uniform coloring (right):
References Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. W. H. Freeman and Company. ISBN 0-7167-1193-1. Uniform and Archimedean colorings, pp. 102–107
External links Weisstein, Eric W. "Polyhedron coloring". MathWorld. Uniform Tessellations on the Euclid plane Tessellations of the Plane David Bailey's World of Tessellations k-uniform tilings n-uniform tilings