A relevant example to the work presented here is polytopal rearrangements arising from a pair of antisymmetric orthogonal bond-angle flexions of a tetrahedral T-4 configuration such as the ε 2 "flex" depicted in Fig. . A traditional analysis based upon this motion would typically only look at the interconverting T-4-S and T-4-R species, and the intermediate square planar SP-4 species. The extrapolation of this trajectory is given in Fig. along with its annotated directed graph representation. In this particular case, the trajectory forms a great circle (largest circle on a sphere) in the configuration space. Depending upon which B-atom pairs that corresponds to, for example, a longitudinal slice through the ϕ = 90° (and equivalently ϕ = 270°) spherical configuration space. This trajectory includes two different orientations of symmetric linear SL-4-2 polytopes. Examination reveals that these symmetric linear SL-4-2 polytopes divide the cycle into two sets of polytopal rearrangements that are equivalent except for their orientations in real space. Given the high energies and bond dissociation associated with symmetric linear SL-4 polytopes, it is understandable that none of the earlier analyses explicitly considered processes that transformed the configurations towards and "through" these. Consequently, the cyclicity of the geometric transformations were not explicitly examined and hence the importance of the orientation permutations within a configuration space not appreciated.