Reflect material system direction-Composite materials

I'm working on a symmetric Carbon laminate mesh (left side|right side). For various reason I have associated some mesh regions of the component to different reference systems, to orient the material system component  along an unique direction. By symmetrical condiction I need to reflect the directional properties on the opposite symmetrical part. It is possible to reflect these directional properties?

Every mesh regions are collect into different sets (and each set are correlated to a different reference system)