Icosahedral Tilings Revisited
  Icosahedral tilings, although non-periodic, are known to be characterized by their configurations of some finite size. This characterization has also been expressed in terms of a simple alternation condition. We provide an alternative proof - shorter and arguably easier - of this fact. We moreover conjecture that the alternation condition can be weakened. 
Nicolas B\'edaride and Thomas Fernique
math.CO