Abstract: In this paper the surface of the octahedron is regarded as composed of pairs of adjacent triangles, or diamond, that tessellate the surface, and thus creates nested diamond subdivision of the surface of the global by quadtree recursive partition. The quadtree Morton coding system is used as the index for addressing the diamonds and for linearizing storage that preserve a high degree of spatial locality. And a method of finding neighbor, ancestors and desendants also is introduced.