Computer Transformations of Correct Polyhedra (Bodies of Plato) to the Semicorrect Polyhedrons (Bodies of Archimed), by the Dint of Autocad System on the Example of Hexahedron and Okrahedron

Abstract

Purpose. To probe interaction of correct polyhedra, to form new, semicorrect forms. To get the formulas of correlations and visual images of polyhedra. Methodology. Researches were conducted by a spatial design in the AutoCAD system. Findings. Certain correlations of sizes and mutual location of bodies of Plato are found – hexahedron and octahedron, at which the bodies of Archimedes are forming. There are truncated hexahedron, truncated octahedron, hexaoktahedron, rombohexaoktahedron, psevdorombohexaoktahedron and truncated hexaoktahedron. The sequence of constructions is expounded, the visual images of the studied objects are got. Originality. In spite ofthe fact that polyhedra were studied by humanity from times of Plato, the use of computer technologies allows to consider the offered theme from the new point of view. Creating polyhedra as hardbodies models, we have got possibility to trace the process of transformation of correct polyhedra in semicorrect. Calculations, resulted in the article, does not meet in literature, consequently offered first. Practical value. It is known that multifaceted forms are widely use in architecture. However, images of polyhedra, executed the methods of engineering graphic arts, areperceived rather difficultly. Therefore the making of spatial models of polyhedra is actual. And the use of computer technologies considerably reduce operating time and gives practically unlimited possibilities of visualization. Materials of the article also can be recommended for the study of stereometry and descriptive geometry.