Perfect colorings of isonemal fabrics using two colors

Abstract

An isonemal fabric is a weaving in which the symmetry group is transitive on the strands. A perfect coloring with two colors is an assignment of the two colors to the strands so that each symmetry operation preserves or reverses the colors. If a transitive group of symmetries has that property we say the coloring is chromatic. We determine (in terms of ‘thin stripings and thick stripings’) the perfect and chromatic colorings for isonemal fabrics using two colors.