The task 3 of forming a network on the sphere from the circles of the same radius

Vladimir Travush,Mariya Chorina,Vasily Antoshkin

doi:10.1051/e3sconf/202017511029

Abstract

one of the methods of formation of geometric networks of arches of the same radius using regular spherical polyhedra is Investigated. The conditions of the task 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 technologies of enlarging assembly. The solution of one variant of the problem of placing a geometric network on a spherical cube and, accordingly, on a sphere is given. Placement on the sphere of arches of one radius, different from placement in the form of meridians, has an effective solution in the form of a network with minimal dimensions of arch segments and nodes of paired arches formed on the basis of circles of identical radii formed on the basis of regular spherical polyhedra. The problem is solved by constructing an independent framework of arches of the same radius on the basis of paired circles of the same radius in the spherical cube system.

Highlights

Abstract: one of the methods of formation of geometric networks of arches of the same radius using regular spherical polyhedra is Investigated
The problem of most of the known solutions of geodesic and mesh domes is a large number of different types of nodes connecting elements of shells, sharp angles of connections, different types and complexity of the support nodes, due to the fact that these support nodes are at different levels, as well as the complexity and laboriousness of the implementation of enclosing structures and roofing
To ensure certainty of the reproduction of the geometry of the domed cover, improve reliability, to simplify the manufacturing nodes of the frame shell and fabrication of building envelopes and roofs, requires the solution of problems associated with a decrease in the number of mounting elements, the reduction of the material of joints, and formation, by optimizing the geometry of the sphere cuts, the location of the supports at the same level of sphere, a significant reduction in the number of sizes of nodes elements

Summary

Introduction

Abstract: one of the methods of formation of geometric networks of arches of the same radius using regular spherical polyhedra is Investigated. As a result of this work, geodesic domes are offered with a specific cuts, which is performed by splitting the faces with large circles along the midpoints of the edges and the centers of the faces of a regular spherical polyhedron, for example, a cube or an octahedron, etc.

Results

Conclusion