Tiling of three-dimensional space is a very interesting and not yet fully explored type of tiling. Tiling by convex polyhedra has been partially investigated, for example, works [1, 15, 20] are devoted to tiling by various tetrahedra, once tiling realized by Platonic, Archimedean and Catalan bodies. The use of tiling begins from ancient times, on the plane with the creation of parquet floors and ornaments, in space - with the construction of houses, but even now new and new areas of applications of tiling are opening up, for example, a recent cycle of work on the use of tiling for packaging information [17]. Until now, tiling in space has been considered almost always by faceted bodies. Bodies bounded by compartments of curved surfaces are poorly considered and by themselves, one can recall the osohedra [14], dihedra, oloids, biconuses, sphericon [21], the Steinmetz figure [22], quasipolyhedra bounded by compartments of hyperbolic paraboloids described in [3] the astroid ellipsoid and hyperbolic tetrahedra, cubes, octahedra mentioned in [6], and tiling bodies with bounded curved surfaces was practically not considered, except for the infinite three-dimensional Schwartz surfaces, but they were also considered as surfaces, not as bodies., although, of course, in each such surface, you can select an elementary cell and fill it with a body, resulting in a geometric cell. With this work, we tried to eliminate this gap and described approaches to identifying geometric cells bounded by compartments of curved surfaces. The concept of tightly packed frameworks is formulated and an approach for their identification are described. A graphical algorithm for identifying polyhedra and quasipolyhedra - geometric cells are described.
The article is devoted to the annual All-Russian scientific and methodological conference "Problems of Engineering Geometry" and the annual All-Russian scientific and methodological seminar "Geometry and Graphics" in 2021. Statistical information about the conference and seminar is provided: the number of participants, universities, the number of cities and countries in which universities are located -participants. Using the expression proposed earlier, the activity of participation of the departments of graphic disciplines in the conference "Problems of Engineering Geometry" and the seminar "Geometry and Graphics", held in 2021, was determined. The comparison of the number of participants and reports of the conference and seminar in 2021 with the number of participants and reports is given and analyzed International Internet conferences "Quality of graphic training" at the Perm National Research Polytechnic University. The results of the All-Russian Seminars "Geometry and Graphics" and the All-Russian Conferences "Problems of Engineering Geometry" of the last two years are compared with each other. In order to compare conferences and seminars quantitatively, not qualitatively, a relationship has been proposed. The content of the reports of the participants of the conference and the seminar is briefly considered. Conclusions are drawn: 1) in 2021, in terms of the success of the seminar "Geometry and Graphics" and the conference "Problems of Engineering Geometry", we managed to move forward - the success rate increased; 2) judging by the number of reports, scientific work on the profile of the department is carried out in a small number of departments. This is due to shortcomings in the staffing of departments of graphic disciplines by teachers. One of them is a lack of understanding that the winners or participants of All-Russian and regional Olympiads who have undergone appropriate training should work as teachers.
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