Bravais quasilattices of icosahedral quasicrystals

A classification of icosahedral quasicrystals based the mutual-local-derivability (MLD) concept is performed. There are eighteen MLD classes within the reservation that the faces of the hyperatoms (windows) are perpendicular to the two-, three-, or fivefold axes. Each MLD class has a representative member to be called the Bravais quasilattice from which the structure of each member of the class is derived by decorating it according to a local rule depending on the member.