To the problem 5 of emplacement of triangular geometric net on the sphere

¹ RAAВS, BolshayaDmitrovka 24-1, Moscow, 107031, Russia
² Mordovian State University, Bolshevistskaya 68, Saransk, 430005, Russia

^* Corresponding author: antovd@mail.ru

Abstract

The sphere creates the minimal surface of enclosing structures and has unique resource saving qualities which makes it indispensable in the construction of “smart buildings». One of the methods of formation of triangular networks in the spherewas investigated. Conditions of the problem of locating a triangular network in the area were established. The evaluation criterion of solution effectiveness of the problem is the minimum number of type-sizes of dome panels, the possibility of pre-assembly and pre-stressing. The solution of the problem of the triangular network emplacement in a compatible spherical triangle on the sphere variant was provided. The problem of the emplacement of regular and irregular hexagons on the sphere, inscribed in a circles, i.e., flat figures or composed ones of spherical triangles with minimum dimensions of the ribs, has an effective solution in the form of a network, formed on the basis of minimum radii circles, i.e., circles on a sphere obtained by the touch of three adjacent circles whose centers are at the shortest distance from each other. The optimization of triangular geometric network on a sphere on the criterion of minimum sizes of elements can be solved by emplacementinthe system the irregular hexagons inscribed in circles of minimal sizes, the maximum of regular hexagons.