Hexagon based grids have gained particular attention in geospatial applications with their use in discrete global gridding systems (DGGS). A feature of many DGGS is the indexing of the grid cells at different resolutions to uniquely identify the cells. For hexagon based DGGS like H3 or IGEO7 the underlying system for indexing is based on 2D generalized balanced ternary (GBT).

GBT was originally described in the 80s for use in image analysis because of the similarity between hexagon grids and biological vision systems. Here we discuss how GBT encodes indexes and discuss the basics of GBT arithmetic in 2D hexagon grids. We demonstrate how GBT arithmetic can be employed for neighbour traversal and more broadly spatial algorithms on hexagonal girds. Finally, we will look at the special cases that arise in the application of GBT to indexing in DGGS, which are the consequences of necessary pentagons and non-GBT arranged base zones.