Wallpaper patterns admissible in itajime shibori

Abstract

Spurred by a study of producing wallpaper pattern types in itajime shibori, this paper explains how the mathematical concept of orbifold places limitations on realizing patterns in this medium. Readers are introduced to the relevant mathematics and artistic processes and their relationships. Each of the seventeen wallpaper patterns is depicted together with its fundamental domain and its orbifold. A theorem shows that at most seven wallpaper pattern types are possible if orbifolds must be folded in three-dimensional space with no cutting. Photographs of itajime shibori dyed versions of all seven are shown in the paper.