A Hamilton cycle in an -cube is said to be -warped if its -paths have their edges running along different parallel -factors. No Hamilton cycle in the -cube can be -warped. The equivalence classes of Hamilton cycles in the -cube are represented by the circuits associated to their corresponding minimum change-number sequences, or minimum -circuits. This makes feasible an exhaustive search of such Hamilton cycles allowing their classification according to class cardinalities, distribution of change numbers, duplicity, reversibility, and -warped representability, for different values of . This classification boils down to a detailed enumeration of a total of equivalence classes of Hamilton cycles in the -cube, exactly four of which do not traverse any sub-cube. One of these four classes is the unique class of -warped Hamilton cycles in the -cube. In contrast, there is no -warped Hamilton cycle in the -cube. On the other hand, there is exactly one class of Hamilton cycles in the graph of middle levels of the -cube. A representative of this class possesses an elegant geometrical and symmetrical disposition inside the -cube.
