Cluster of diamond-like structures as Euclidean realization of some constructions in projective geometry (Q1417746)

A simplex of the three-dimensional Euclidean space \(E^3\) is a tetrahedron, in particular a diamond-like structure. The goal here is to demonstrate that graphs of a certain structure of projective geometry are realized in \(E^3\) as graphs of some special clusters. The Galois field \(\mathrm{GF}(q)\) unambiguously determines an incidence table of the final projective plane \(\mathrm{PG}(2,q)\), subtables of which enable to construct bichromatic graphs of hexacycle clusters with nodes at the sphere \(S^2\).