Question related to hexagonal partitions of cartographic/geographic space, hexagonal sampling systems and hexagonal rasters.
There are only three regular geometrical shapes capable of partitioning a plane in equal cells: the equilateral triangle, the square and the hexagon. Even though squares have historically been the preferred choice in GIS (particularly in raster data formats) hexagons present a number of advantages that justify its usage:
Unequivocal and isotropic neighbourhood.
Higher spatial resolution with same area cells.
Faster computation to/from the Fourier spectrum.
Fidel modelling of fluid dynamics.