One of the essential numerical laws of the geometric network of shape development

Abstract

A network for the hypohexagonal type was established and it was shown that the numerical law of the development of forms is essentially the same for this network, although now the faces are expressed by symbols not of three, but of four numbers; from these four you can always choose three, including the necessary the first number, which will be completely identical to the numbers of the first network. But even if we do not make such a selection, but limit ourselves to three numbers, of which one is in first place, and we choose the other two arbitrarily (that is, the second with the third , or the second with the fourth, or finally the third with the fourth), then the law in question here will still remain valid. Of particular importance is the distribution of even and odd numbers. This law is that of the seven symbols relating to any elementary triangle of the network, one certainly encloses three (that is, all), three encloses two, and three encloses one odd number; all other numbers of symbols are even.