A new invariant was proposed which classified phase defects in Penrose tilings. This invariant took values in a group which was closely related to the fundamental group of a certain topological space that was the image of the tiling itself under identifications that were dictated by matching rules. This space played the role of an order parameter for pentagonal quasicrystals. The invariant permitted one to discriminate between mismatches of differing directions.

T.S.Misirpashaev: Journal de Physique I, 1995, 5[3], 399-407