Colored lattices
AUTOR(ES)
Harker, David
RESUMO
Combinations of translations and color permutations are derived that leave a periodic array of colored points—a colored lattice—apparently unchanged. It is found that there are three types of colored lattices: (1) those in which all rows and nets have more than one color, (2) those in which there are rows with only one color, and (3) those in which there are both rows and nets with only one color. The color permutation groups of colored lattices are all Abelian. The direct product of three independent cyclic subgroups is required by type 1, but only two are required by type 2; in type 3 the color permutation group consists of the n powers of a cyclic permutation of all n colors present—i.e., the group consists of a single cycle.
