This paper presents some results of the first investigations on the application of the recently discovered existence of Phi (F ) relationship within a regular hexagonal tessellation and is based on the influence of this geometric relation on the analysis and synthesis of structural systems. The vertices of the lattice have been determined as the Phi (F ) centers with high precision and meet the variance from Phi (F ) in accordance with the 11-th series of the Fibonacci convergence sequence on Phi (F ). Using centered geometric constructions an interrelation of logarithmic spirals and isolines of vertices like Phi (F ) centers within such an endless regular grid with variable dimensions of hexagons which circumradii increase or decrease in geometric progression has been derived. It is geometrically proved having a self-similarity and an integer dimension within a hexagonal grid, which allow investigating them like fractals or plane-filling curves.