Abstract: The paper describes the Octahedron-based Aperture 4 Hexagonal DGGS (OA4HDGGS) using the set theory. By defining two basic operations, the dual and the central subdivision, recursive relation, nested relation and hierarchical relation between the set of hexagonal grids and the set of triangular grids are established. Location of the hexagonal cell on triangular face is described in the three-axes integral grid coordinate system, and meanwhile, essential problems of index schema, including the calculation of Cartesian coordinates of the cell, the determination of neighbors, children and parents of the cell, are solved by a few theorems. According to the theorems, indexing algorithms are proposed and validated by contrastive experiments. The experimental results show that our indexing schema is 600 times faster than similar schema, which proves it is more suitable for computer processing.