Abstract
The problem of random close packing has been analyzed as a task of self-development with the doubling of the scale at the stage of becoming. It has been shown that the site of a transforming body at this stage can be described by hexagons in the two-dimensional case and by tetrakaidecahedra in the three-dimensional case. When their vertices, equidistant from the center, are distributed so that the smallest distance between them is largest among its all possible values, the fraction of the surrounding Euclidean space, which is occupied by the figures, coincides with the capacity of a random close packing. The capacity takes the value 0.827, in the two-dimensional case, or one of the two values, i.e., 0.6366 and 0.6457, in the three-dimensional case. The result obtained provides insight into the geometric meaning of the isotropic random close packing and serves to accept the existence of its two forms in the three-dimensional case.
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