Cluster Self-Organization of Intermetallic Systems: New Clusters-Precursors K6 and K3 for the Crystal Structures of the Sr12Mg20Ge20-oP52, Sr2LiInGe2-oP24, and Sr2Mg2Ge2-oP12 Family

Using computer methods (the ToposPro software program), a combinatorial-topological analysis and modeling of the self-assembly of crystal structures of the Sr₁₂Mg₂₀Ge₂₀-oP52 (a = 21.707 Å, b = 4.483 Å, c = 18.456 Å, V = 1795.88 ų, Pnma), Sr₂LiInGe₂-oP24 (a = 7.503, b = 4.619, c = 17.473 Å, V = 605.63 ų, Pnma), and Sr₂Mg₂Ge₂-oP12 (a = 10.882 Å, c = 5.665 Å, V = 670.8 ų, Pnma) families is carried out. For the crystal structure of Sr₁₂Mg₂₀Ge₂₀-oP52, 17 variants of the cluster representation of a 3D atomic grid with 2 (5 variants), 3 (6 variants), and 4 (6 variants) structural units are established. The variant of the self-assembly involving the triple rings K3 = 0@3(SrMgGe) and K3 = 0@3(Mg₂Ge) and double tetrahedra K6 = 0@6(Sr₂Mg₂Ge₂) with symmetry –1, forming a suprapolyhedral cluster-trimer A from clusters (SrMgGe)(Sr₂Mg₂Ge₂)(SrMgGe) and the cluster trimer B from clusters (Mg₂Ge)(Sr₂Mg₂Ge₂)(Mg₂Ge), is considered. For the crystal structure (Sr₂Li)₂(InGe₂)₂-oP24, framework-forming polyhedra in the form of double tetrahedra K6 = 0@6(Sr₂Mg₂Ge₂) and triple rings K3 = 0@3(SrMgGe) are defined. For the crystal structure of Sr₂Mg₂Ge₂-oP12, the framework-forming polyhedra are defined in the form of double tetrahedra K6 = 0@6(Sr₂Mg₂Ge₂). The symmetry and topological code of the processes of self-assembly of 3D structures from clusters-precursors has been reconstructed in the following form: primary chain → layer → framework.