In total, there are 12 systems, 60 point groups and 89 single forms in crystals and quasicrystals. Among them, 5 new systems, 28 new point groups and 42 new single forms belong to quasicrystals, while the other 7 syst...In total, there are 12 systems, 60 point groups and 89 single forms in crystals and quasicrystals. Among them, 5 new systems, 28 new point groups and 42 new single forms belong to quasicrystals, while the other 7 systems, 32 point groups and 47 single forms belong to crystals. In this paper, the point groups and single forms of quasicrystals are deduced and drawn as stereographic projections by the rules of crystallographic point groups. These stereographic projections integrate the crystal and quasicrystal symmetry theories.展开更多
文摘In total, there are 12 systems, 60 point groups and 89 single forms in crystals and quasicrystals. Among them, 5 new systems, 28 new point groups and 42 new single forms belong to quasicrystals, while the other 7 systems, 32 point groups and 47 single forms belong to crystals. In this paper, the point groups and single forms of quasicrystals are deduced and drawn as stereographic projections by the rules of crystallographic point groups. These stereographic projections integrate the crystal and quasicrystal symmetry theories.
