Polytopal rearrangement trajectories through the configuration space reveal orientation permutations Traditional analyses of polytopal rearrangements have tended to focus on very small regions of their configuration spaces and ignored the orientations of the species involved despite the term pseudorotation suggesting a species' orientation in real space being important. Analyses like the one given in this work, equip us with a full map of the corresponding configuration space from which we can see all possible configurations. Consequently, it becomes both possible and instructive to take the results of the earlier analyses and extrapolate their trajectories through the full configuration space.