A self-similar ordered structure with a non-crystallographic point   symmetry
  A new class of self-similar ordered structures with non-crystallographic point symmetries is presented. Each of these structures, named superquasicrystals, is given as a section of a higher-dimensional "crystal" with recursive superlattice structures. Such structures turn out to be limit-quasiperiodic, distinguishing themselves from quasicrystals which are quasiperiodic. There exist a few real materials that seem to be promising candidates for superquasicrystals. 
Komajiro Niizeki and Nobuhisa Fujita