Number of Symmetrical objects in n-dimensional space with different layers

摘要

Though there are numerous results on most efficient way to pack symmetrical objects (circles, spheres etc.) with calculation of packing factors, there is no formula to count number of such objects in symmetrical configuration in n-dimensional space. We present here an empirical formula for total number of symmetrical objects in n-dimensional space with different layers. The formula is tested for one, two and three dimensional space with experiment.