Network from the circles of the same radius for sustainable energy-efficient roof structures

Abstract

In this research paper, we investigated one of the methods of formation of geometric networks of arches of the same radius using regular spherical polyhedra. The variants of cutting sustainable energy-efficient coatings of buildings in the form of spherical domes are proposed. The task conditions of placing the specified network on the sphere are set. The criterion for evaluating the effectiveness of solving the problem is the minimum number of standard sizes of segments of the dome arches, the possibility of using pre-assembly technologies. The solution of one variant of the problem as placing the network on a spherical icosahedron and, accordingly, on a sphere is given. The placement of arches of one radius on the sphere, different from the location in the form of meridians, has an effective solution in the form of a network with minimal dimensions of arch segments and with nodes of paired arches comprised on the basis of circles of the same radii formed on the ground of regular spherical polyhedra. The problem is solved by constructing and combining in a system of regular spherical polyhedral with independent frameworks of arches of the same radius on the basis of paired circles of equal radius.