Abstract: The symmetry is concerning basic rule, which must be followed when the integer was constructed by parts. The pleasant impression of the thing was materialized by the consonance between the integer and the parts. The symmetry rules were exerted perfectly in crystallography. The space group theories of traditional crystallography still have leading meaning for crystal structure determination in current crystallography. The symmetry characters of quasiperiodic crystals and incommensurable phases were discussed. The possibility was suggested that the plane constitute in art was designed using the plane group theory in crystallography.