Abstract
The process of hierarchical filling of space by p-dimensional regular polytopes is considered under the condition of large-scale discrete increase in the size of polytopes and preservation of their shape (scaling process). It is shown that the polytopic prismahedrons are a concrete realization of the stereohedrons. The polytopic prismahedrons have the necessary properties for translational filling of spaces of higher dimension without slits face to face. Moreover, it is proved that the polytopic prismahedrons forming such fillings can have common elements of any dimension included in the polytope. On the basis of the research carried out in spaces of higher dimension, a new paradigm for describing a discrete world has been put forward.
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