Symmetry is graded as Excellent, Very Good, Good, Fair or Poor on a GIA report. When polishing a rough diamond, the aim is to cut the heaviest, most valuable diamond possible. This often means polishing a diamond with imperfect symmetry to avoid inclusions or just leaving more weight to achieve an even carat weight, such as 1.00 ct. The polished diamond may be slightly off round, have variations in girdle thickness, tilting of the table, and off centering of the table or the culet.
Very few diamonds are perfectly symmetrical, but symmetry is less important to the overall beauty of a diamond than the critical facet proportions. You may never notice any difference between diamonds with excellent or ideal and very good or good symmetry.