Sentence:  This case suggests that the alternation of a polyhedron should be bounded by actual vertex figures and <WSD>alternated</WSD> faces. The case of the cube is in agreement with this notion, since the <WSD>alternated</WSD> square is nothing. 
Meaning of the word marked with <WSD> tags:  To perform an alternation (removal of alternate vertices) on (a polytope or tessellation); to remove vertices (from a face or edge) as part of an alternation.