Boron-based quasicrystals with sevenfold symmetry

It is not too surprising that 5-fold symmetry is the symmetry of quasicrystals since icosahedral coordination is the most frequent atomic environment type (AET) in intermetallic phases. What about AETs with 7-fold symmetry? Whereas no regular or semi-regular polyhedra (Platonic or Archimedean solids) exist with rotational symmetry larger than 5-fold, polyhedra with only axial n-fold symmetry (e.g. pyramids) are possible for arbitrary n. Indeed, (distorted) seven-membered rings are very common in ternary borides and borocarbides such as the YCrB4, ThB4, ThMoB4, Y2ReB6 structure types. The possibility to find heptagonal quasicrystals related to these phases will be discussed.