News Academy of Engineering Sciences A.M. Prokhorov Annotation << Back Part 2. Application of group of symmetry four-dimensional cube and its subgroups for classification of electronic states in crystals Four-dimensional representations of subgroups of group of Lorentz and Shubnikovsky groups Kustov E.F. Muravyev E.N. In work groups of symmetry 4 -dim spaces which are subgroups of group of 4-dim cubes are developed. 4-dim elements of symmetry are developed where as 4th dimention is time and representations of groups of magnetic symmetry and Shubnikovsky groups are created. Tables of characters of these groups and the scheme of a reduction of these groups on their subgroups are created. The method of classification of multielectronic states with use of groups of four-dimensional space taking into account spatial and time symmetry is developed. Parities of reduction irreducible representations of groups of four-dimensional space are received: orthogonal group O4 , group of pure rotations R4 on groups of four-dimensional cube O4h and octahedron О4, three-dimensional groups cubic and hexagonal singonies: Oh, D6h. Four-dimensional classification of levels of spin – orbital interaction of RE ions is spent at an intermediate reduction on group of a four-dimensional cube. Key words: four-dimensional multi-polyhedron, 4-cube, 4-octahedron, 4-tetrahedron, magnetic group, reduction symmetry; 4D and 3D point groups. Contacts: E-mail: kustovyf@mail.ru Pp. 22-28.