a cube has six faces and twelve edges. you start at one corner, are allowed to move only along the edges and may not retrace your path along any edge. Consistent with these rules, there are any number of ways to arrive back at your starting point. For instance, you could move around the four edges that make up one of the square faces. The four corresponding displacement vectors would add to zero. How many ways are there to arrive back at your starting point that involve eight displacement vectors that add to zero? Describe each possibility, using drawings for clarity. _{}^{}

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