Investigation of the asymptotic series of heights of regular simplices with increasing dimensionality of euclidean space

The problem of spherical packing and the distribution points on a sphere are well-known unsolved mathematical problems. In particular, is included in list problems Steve Smale. Accordingly, significant interest for study both direct search solutions to research areas related known dense coating directly regular, irregular layered lattices, noise-resistant coding, synthesis analysis broadband signals, multidimensional spaces, crystallography, methods solving differential equations calculating n-dimensional integrals, many other particular entire fields knowledge. paper presents results studies some properties regular simplex Euclidean space. vectors forming define fundamental basis hexagonal lattice. subject regularities vector object space, novelty lies formulated proven theorem, several formulas that allow recursive non-recursive calculations characteristics packages. an simplex. Main theorem asymptotic character sequence heights with increasing dimension space proved, consequences remarks supplementing formulated. conclusion article contains additions numerical examples comments results. practical significance proposed tools contribute development theory geometric objects