Abstract: While existing methods for 3D surface approximation use local geometric properties, we propose that more intuitive results can be obtained by considering global shape properties such as symmetry. We modify the Variational Shape Approximation technique to consider the symmetries, near-symmetries, and partial symmetries of the input mesh. This has the effect of preserving and even enhancing symmetries in the output model, if doing so does not increase the error substantially. We demonstrate that using symmetry produces results that are more aesthetically appealing and correspond more closely to human expectations, especially when simplifying to very few polygons.