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 & Aring;, b = 4.483 & Aring;, c = 18.456 & Aring;, V = 1795.88 & Aring;(3), Pnma), Sr2LiInGe2-oP24 (a = 7.503, b = 4.619, c = 17.473 & Aring;, V = 605.63 & Aring;(3), Pnma), and Sr2Mg2Ge2-oP12 (a = 10.882 & Aring;, c = 5.665 & Aring;, V = 670.8 & Aring;(3), 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.