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Abstract: One of the key concepts of the school geometry course is the concept of “polyhedron”. Throughout the history of the study of polyhedra, scientists have identified more and more complex types of them. So, in ancient works, mainly regular polyhedra are presented, in a later time the emphasis was on the study of prisms and pyramids, and at the present stage not only convex, but also stellate, homogeneous and semi-homogeneous polyhedra are studied. In this regard, the scientific presentation of this concept, as well as its definition in every foreseeable historical moment, has changed. The selection of its characteristic properties and their description in the educational literature is methodologically difficult for the authors of textbooks. Great contribution to the representation of the concept of “polyhedron” in domestic textbooks made famous mathematician A. D. Aleksandrov. In 1981, in the journal “Mathematics in School”, he analyzed the then existing definitions of this concept in school textbooks on geometry and proposed his own definition, which covered a wider class of polyhedral. This article describes an analysis of how the definitions of the basic concepts of the theory of polyhedra, their volumes and content in the school geometry course have changed since the publication of A. D. Aleksandrov to the present. Analyzed are modern school textbooks included in the Federal List recommended for use in the implementation of general education programs. The description of the analysis of the pedagogical experiment, the purpose of which was to test the formation of the concept of a polyhedron in school graduates. It is proposed to carry out a qualitative analysis of the connections of this concept with other concepts of such theories as graph theory, groups, computational geometry in the project or circle activities of students.