Octahedral and tetrahedral patterns in structural mineralogy – nature’s answer to L. Pauling’s fifth rule

Research subject. Structures of minerals with filled octahedral, tetrahedral, and trigonal voids in anionic packages. Aim. Analysis of the correlation of L. Pauling's rule of parsimony with variety of minerals. Key points. Using the example of the interrelation between following crystal structures: olivine, norbergite, chondrodite, humite, clinohumite, СdI 2 , Mg(OH) 2 , rutile, brookite, anatase, spinel, diaspore, goethite, groutite, stenierite, ramsdellite, VO 2 , hollandite, todorokite, romanechite, corundum, karelianite, eskolaite, hematite, tetradymite, ilmenite, calcite, magnesite, siderite, rhodochrosite, dolomite, kutnohorite, ankerite, topaz, wurtzite, sphalerite, chalcopyrite, stannite, germanite, enargite, sulvanite, pentlandite, litharge, LiOH, cuprite, cooperite, chalcocite, BCl 3 , Na 3 As, covellite and domeykite, a variety of possible topological structures of crystal structures with the presence of various voids in a tightly packed motif of anions, which can be occupied by smaller cations, is demonstrated. Octahedral motifs of various stoichiometry of the ratio of ions forming the package to filled voids, tetrahedral motifs with layers of the same parity and different parity, anion-centered tetrahedral motifs, and trigonal motifs are analyzed. Conclusions. The explanation for the apparent contradiction between the observed topological diversity of polyhedral motifs and L. Pauling’s fifth rule is given.