Abstrac In many geometries we observed the following situation. There ia a non-empty set P of geometric objects (like points, lines, planes, circles etc.) and a distinct set A of permutations of P (like collineatio, motions, automorphisims etc. ) such that for any tow objects a,b there is exactly one permutation in A denoted by [a?b] mapping a onto b. The pair (P,A) is called regular permutation set . uch a situation we obtain for instance if we take for P the set of all points of Euclidean, or more generally an absolute geometry and for A, all reflection in points. More precisely, many geometries (P, A, ?) (P denotes the set of points, A the set of lines and ? stands for the congruence relation) . A set P together with a subset A? Sym P is called symmetric permutation set denoted by (P,A) if for each a,b in P there exists a unique permutation ? in A such that ?(a)=b and ?(b)=a.