White, D. 2000. Global grids from recursive diamond subdivisions of the surface of an octahedron or icosahedron. Environmental Monitoring and Assessment 64(1):93-103.
In recent years a number of methods have been developed for subdividing the surface of the earth to meet the needs of applications in dynamic modeling, survey sampling, and information storage and display. One set of methods uses the surfaces of Platonic solids, or regular polyhedra, as approximations of the surface of the earth. Diamond partitions are similar to recursive subdivisions of triangular faces of either the octahedron or icosahedron. This method views the surface as either four (octahedron) or ten (icosahedron) tessellated diamonds, where each diamond is composed of two adjacent triangular faces of the figure. The method allows for a recursive partition on each diamond, creating nested sub-diamonds, that is implementable as a quadtree, including the provision for a Peano or Morton type coding system for addressing the hierarchical pattern of diamonds and their neighborhoods, and for linearizing storage. Furthermore, diamond partitions, in an aperture-4 hierarchy, provide direct access through the addressing system to the aperture-4 hierarchy of hexagons developed on the figure. Diamond partitions provide a nested hierarchy of grid cells for applications that require nesting and diamond cells have radial symmetry for those that require this property. Finally, diamond partitionscan be cross-referenced with hierarchical triangle partitions used in other methods.