About the generalized symmetry of geometric figures weighted regularly and easily by „physical” scalar tasks

Abstract

Let us have geometrical figure F with discrete group of symmetry G and finite set N = {1, 2, ..., m} of „indexes”, which mean a non-geometrical feature. On fix a certain transitive group P of permutations over N. We will note with the symbol Fi the intersection of geometric figure F with the fundamental domain Si of the group G. Ascribe to each interior point M of Fi the same „index” r from the set N . We obtain one figure F(N), weighted regularly and easily with summary load N.