For hexahedral meshes, it is difficult to make topological modifications which preserve conformal property and which are local to the modified elements. This is most easily understood in how changes affect the dual surfaces ("sheets") and lines ("chords"), which have nonlocal extent in hexahedral meshes. A set of three operations is proposed which represent distinct local changes to the hex mesh and its dual. These operations are shown to compose the larger set of "flipping" operations

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... by Bern et. al. The relation between these dualbased operations and the insertion of a Boy surface in the dual, described by Bern, is also discussed. 4 Although this is accepted as conventional wisdom in some circles, there is virtually no publication record to support this view. It would be quite helpful if there was a rigorous explanation for why hex meshes perform better than tetrahedral meshes in specific cases.