Superquasicrystals: selfsimilar ordered structures with   non-crystallographic point symmetries
  We present a systematic method of constructing limit-quasiperiodic structures with non-crystallographic point symmetries. Such structures are different aperiodic ordered structures from quasicrystals, and we call them "superquasicrystals". They are sections of higher-dimensional limit-periodic structures constructed on "super-Bravais-lattices". We enumerate important super-Bravais-lattices. Superquasicrystals with strong selfsimilarities form an important subclass. A simplest example is a two-dimensional octagonal superquasicrystal. 
Komajiro Niizeki and Nobuhisa Fujita