The results of x-ray diffraction studies of preserved zincite samples subjected to dynamic compression (28 GPa) and the powder patterns of hydrothermally grown ZnO crystals are presented. Three new modifications have been synthesized: ZnO(I, II, III). The x-ray diffraction pattern of ZnO(I) is indexed in the hexagonal unit cell with a = 4.121(2) Å, c = 15.114(5) Å, V = 222.3 Å 3 , Z = 12, r calc = 7.293 g/cm 3 , Fedorov group P6 3 /mmc. The x-ray diffraction data for ZnO(II) are indexed in an orthorhombic subcell with a = 5.997(2) Å, b = 5.267(1) Å, c = 2.369(1) Å, V = 74.8 Å 3 , Z = 4, r calc = 7.222 g/cm 3 . The x-ray diffraction pattern of ZnO(III) is indexed in the primitive monoclinic cell with a = 7.931(8) Å, b = 7.911(4) Å, c = 2.995(1) Å, b = 91.07(4)°, V = 188 Å 3 , Z = 8, r calc = 5.749 g/cm 3 .According to the geometric model an ionic crystal consists of ionic spheres with a definite radius. Each coordination polyhedron (icosahedron, cube, octahedron, tetrahedron, regular triangle) has a critical (minimum) ratio R c /R a of the radii of the cation and anion with which it can be formed (anions touch cations as well as one another).The probability of any particular coordination of the cations can be estimated by means of the MagnusGoldschmidt criterion: a coordination polyhedron forms in a structure if the ratio R c /R a is greater than a critical value.The ratio R c /R a = 1 for an icosahedron, 0.731 for a cube, 0.414 for an octahedron, 0.225 for a tetrahedron, and 0.155 for a triangle.The environment of zinc can be octahedral in compounds containing oxygen, since the ratio of the ionic radii of zinc (0.74 Å) and oxygen (1.36 Å) is 0.544 and falls into the interval 0.414 -0.732.A solid solution with NaCl type structure is formed when zincite dissolves in CoO and NiO. Synthesis of pyroxene ZnSiO 3 according to the reaction ZnO + SiO 2 ® ZnSiO 3 is accompanied by an increase of the coordination number ZnO 4 ® ZnO 6 . However, at atmospheric pressure the environment of zinc in most compounds is tetrahedral. The enthalpy of a coordination change (ZnO 4 ® ZnO 6 )DH = 24.5 ± 3.6 kJ/mole, calculated from thermochemical data for a series of compounds and solid solutions, indicates that the preferred symmetry of oxygen atoms surrounding zinc is tetrahedral [1].A tetrahedral environment around zinc is observed in zinc sulfide under normal conditions. Sphalerite and wurtzite modifications of this compound, where each atom is surrounded by an almost regular tetrahedron formed by atoms of the other type, are encountered in nature. Sphalerite (a-ZnS) crystallizes in the cubic system with a = 5.409 Å, V = 158.2 Å 3 , Z = 4, volume per formula unit (V/Z ) = 39.6 Å 3 , and Fedorov group F43m (3C).The lattice of a-ZnS can be regarded as two face-centered cubic lattices shifted relative to one another by onefourth the diagonal of a cube. The zinc and sulfur atoms in the sphalerite structure occupy the sites of these sublattices, which possess the symmetry of a tetrahedron (43m).In the space group F43m the number of formul...