Bingham and Muchisky (submitted) found that observers were very accurate in determining the location of the center of mass in planar objects. They found that systematic errors were affected primarily by object orientation while random errors varied with amounts of symmetry. However, different types of symmetry seemed to affect errors in different ways. We constructed objects that reproduced the axial reflective symmetries of objects used previously. In a corresponding set of objects, we perturbed the symmetries to eliminate axial reflective symmetry leaving only rotational symmetries. Random errors decreased in all directions with increasing rotational symmetry. Axial reflective symmetry further reduced errors in the direction perpendicular to the axis. Different types of symmetry were used and had different effects. We replicated the effect on systematic error of orientation. However, we also found an effect of the perturbation of symmetry that suggested that observers used an approximation to symmetry.
We constructed a series of objects in which axial reflective symmetry was established and then perturbed by varying amounts. We found that systematic errors were structured by the underlying approximate symmetries. We discussed the problem of quantifying symmetry.