**Authors:** Palistrant A. F.

### Abstract

The geometrical principle of the classification of $P$-symmetries permits to distinguish sharp 31 the $P$-symmetry of two-sides rosettes, when the group of the substitutions is isomorphic to one of the crystallografic symmetrical groups of two-sided rosettes $G_{320}$. The two-sided rosette $P$-symmetries revealed are recorded in convenient for using symbols and were used for generalization of the frieze $G_{21}$ groups. The exactly 2597 different groups of the symmetry of $G_{5421}$ category in the 5-dimensional of the Evklid space was establihed by means of discovered frieze $G^P_{21}$ groups of the 31 two-sided rosettes.