Novel topological and geometrical modelling of N-frequency geodesic icosahedron tensegrities

We propose a novel graph-theoretical method for efficient generation of the topological structure of N-frequency geodesic icosahedron tensegrities. The method only requires the adjacency list of edges of an N-frequency icosahedron, and using a sophisticated approach, creates the major topological entities of the corresponding geodesic icosahedron tensegrity. The graph theory is used to build a bridge between a regular icosahedron and its dual complex tensegrity. The approach proposed is general and perfectly works on icosahedrons with any degree of frequency. The generation of edges is managed in such a way that enables us to group them in different sets as cables and struts. The spherical geodesic tensegrities generated using our method could remarkably extend the complex data sets and large-scale benchmark models required for researchers in the field of tensegrity structures. The whole process and its parts are described and illustrated step by step. Furthermore, the form-finding of 1 to 5-frequency geodesic icosahedron tensegrities is also performed, and sets of self-equilibrium force densities corresponding to their super-stable geometries are provided. The results clearly demonstrate the effectiveness of the proposed method for automated modelling of the icosahedron tensegrities with a chosen frequency.

Automated summary

We propose a novel graph-theoretical method for efficiently generating the topological structure of N-frequency geodesic icosahedron tensegrities. The method is applicable to icosahedrons with any frequency, and it allows for the generation of complex data sets and large-scale benchmark models. The entire process and its components are described and illustrated step by step, and form-finding of 1 to 5-frequency geodesic icosahedron tensegrities is also performed, providing sets of self-equilibrium force densities corresponding to their super-stable geometries.