Russian Federation
Russian Federation
Polyhedrons, as one of the types of spatial forms, are of considerable practical interest and, due to this, are widely reflected in various fundamental and applied sciences, in engineering, architecture and design. Polyhedrons can be found in the designs of machine parts, machines and tools. They are also used in the design of complex technical structures, industrial and residential buildings, industrial design objects and jewelry. Convex polyhedrons are of the greatest practical interest. This study substantiates the need for a more in-depth study of the topic «Polyhedra» in the course «Engineering Graphics» for undergraduate students of some areas of Peter the Great St. Petersburg Polytechnic University (SPbPU) due to the specifics of their area of training and further use in practical activities. The article provides an analysis of the degree of disclosure of the topic of polyhedra in the course of stereometry in high school and in the discipline "Engineering graphics" studied at the university. The article shows the results of a statistical study conducted by the authors to control residual knowledge on the topic of «Polyhedra» in the school course of stereometry based on a survey of students from various areas of SPbPU. The purpose of the survey is to identify issues that require clarification and additions when studying the section «Descriptive Geometry» of the discipline «Engineering Graphics». The assessment of knowledge was carried out according to three selected criteria: knowledge of the main types of polyhedra, understanding the topology of regular polyhedra, previously acquired skills in constructing sections of polyhedra (cube) with a plane in an axonometric projection. An attempt was made to systematize convex polyhedra by their degree of regularity in a single classification, combining some provisions of the school course of stereometry and the section «Descriptive Geometry» of the discipline «Engineering Graphics» studied in higher educational institutions. A classification is presented with a detailed description of the designs of various polyhedral shapes and their main characteristics. The classification does not pretend to be a final version, and can be supplemented with polyhedra with other classification features, for example, by the shape of the faces or their inscribeability in a sphere. Separately considered are various types of prisms, pyramids and prismatoids, which are of the greatest practical interest and are studied in detail in the school course of stereometry and the section «Descriptive Geometry» of the discipline «Engineering Graphics» mastered at the University.
classification of polyhedra, Archimedes' solids, semiregular polyhedra, duality of polyhedra, Platonic solids, Catalan solids, Johnson solids
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