Prospects for the use of one-sided surfaces in design practice

Abstract

The article provides examples of using one-sided surfaces, which are completed static structures with surfaces turned inside out, in design practice. One-sided surfaces are the objects of study of topological mathematicians, but in recent years these surfaces have been employed in their research by physicists and chemists. One-sided surfaces include the following surfaces: the Mobius strip, the Klein bottle, the heptahedron and the Steiner surface. One-sided surfaces were discovered and studied by German mathematicians A. Mobius and J. Listing independently of each other in the middle of the 19ᵗʰ century. The first patents for the engineers» inventions, which used the properties of one-sided surfaces, appeared in the 20ᵗʰ century. The latest scientists» achievements in the field of physics and chemistry, awarded the Nobel Prize, were obtained by using the properties of one-sided surfaces. The material of the article will allow drawing the attention of design engineers to one-sided surfaces when creating new machines and improving technological processes. Layouts of these surfaces are printed on a 3D printer using electronic models of the Mobius strip, the Klein bottle and the heptahedron.