The symmetrical properties of a group of vertices are leveraged to reconstruct the group using vertex data for a subset of the vertices and a set of control data. The subset of vertices is symmetrical to one or more other subsets of vertices in the group, and the control data includes information to reconstruct the one or more other subsets using the vertex data for the first set of vertices and symmetrical characteristics of the group. In some embodiments, reconstruction is performed using a geometry shader in a graphics processor to compute the additional vertices.