Say I live in a very large, fixed radius, three-sphere. Could a mathematician pick a very large set of points at the right locations in my three-sphere such that when each point was connected to their nearest 6 neighbors with short line segments that locally I would have a nearly rectangular 3 dimensional grid that would also be uniform in the sense that from any point the grid would look the same, lengths of line segments all the same and angles between nearest line segments nearly or exactly 90 degrees? Would be some kind of translation in-variance? Would this be in effect "chopping" up a three-sphere into little cubes? Is there a smallest number of cubes that a three-sphere can be chopped into or do we only get cubes when the number of cubes is very large? Thanks for any help!