Symmetry in Armenian Mediaeval Ornaments

Abstract

The Armenian mediaeval culture is a treasure of ornaments. Sacral architecture, stone and wood carvings, decorations on paper and fabric, all contain planar periodic patterns. For the first time we classify the available ornaments according to their symmetry properties with the tools of mathematical group theory. We determine the unit cells of patterns, axes of rotation, mirror and glide reflections, all symmetry operations that preserve the pattern invariant. The results show that of seventeen crystallographic plane groups, four do not exist. Other symmetry groups are represented in a more or less balanced distribution with a dominance of fourfold symmetry. The distribution of the symmetry groups can be used to rigorously compare different cultural groups. Armenia, with its geographical location along the Silk Road, was inspired by different cultures and served as a source of inspiration for many cultures. The mathematical analysis of ornaments is an objective measure to follow such interactions.