Symmetry ratios and structural code of layered crystals of the family [(Ge,Sn,Pb)(Te,Se)]$_{m}$[(Bi,Sb)$_{2}$(Te,Se)$_{3}$]$_{n}$ ($m,n$ = 0,1,2 $\dots$)

The crystal structures of layered crystals, i.e. ternary alloys [(Ge,Sn,Pb)(Te,Se)]$_{m}$[(Bi,Sb)$_{2}$(Te,Se)$_{3}$]$_{n}$ ($m,n$ = 0,1,2 $\dots$) (space groups $R\bar3m$, $P\bar3m_1$, and $P2_{1}/m$) are analyzed. The hierarchical relations between various space groups of ternary alloys are determined. The structural code of crystals of the family is determined, which takes into account their composition, crystal structure, and thermodynamic stability of layer stacks forming the superstructures.