1.verbTo perform by turns, or in succession; to cause to succeed by turns; to interchange regularly.
2.verbTo happen, succeed, or act by turns; to follow reciprocally in place or time; followed by with.
"The flood and ebb tides alternate with each other."
3.verbTo vary by turns.
"The land alternates between rocky hills and sandy plains."
4.verbTo 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.