The method of object symmetry (Mardia et al. 2000) has been elaborated for the studies of shape variation in structures that have an internal plane of bilateral symmetry (e.g. vertebrate skulls and insect bodies). Further work related object symmetry to the structure of the shape tangent space (Kolamunnage & Kent 2003, 2005). For instance, principal component analysis (PCA) can separate a compo...