Answer:
A. when the plane passes through a pair of vertices that do not share a common face
Step-by-step explanation:
The cross section will be a parallelogram if two pairs of opposite faces are intersected. Having the plane contain the space diagonal, but no other vertices, is one way to ensure a (non-rectangular) parallelogram.
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The only vertices not sharing a common face are the ones at opposite ends of a space diagonal. If the plane intersects both of those, it will contain the space diagonal.
