Deriving one of the basic formulas of the doctrine of symmetry

Abstract

The formula in question here is a logical consequence of two already known formulas, which were given in full by the author of the doctrine of symmetry, namely in the part that was published under the title “Symmetry of Finite Figures.” The formula, applicable to any group of symmetry axes (type of alignment symmetry), but of course not applicable to one axis taken separately, makes it possible to directly derive the value of symmetry from the number of symmetry axes. From it, by the way, it follows that the value of the symmetry of the combination is certainly even (which is understandable, in view of the obligatory presence of double axes of symmetry in the aggregates), and therefore the value of the symmetry of those types where, in addition to the axes of symmetry, the elements of direct symmetry are also included, is certainly divided by four