alternating

Verb

alternate (third-person singular simple present alternates, present participle alternating, simple past and past participle alternated)

1. (transitive) To perform by turns, or in succession; to cause to succeed by turns; to interchange regularly.
   • The most high God, in all things appertaining unto this life, for sundry wise ends alternates the disposition of good and evil.1701, Nehemiah Grew, Cosmologia Sacra
2. (intransitive) To 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. (intransitive) To vary by turns.
   • The land alternates between rocky hills and sandy plains.
4. (transitive) 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.
   • This case suggests that the alternation of a polyhedron should be bounded by actual vertex figures and alternated faces. The case of the cube is in agreement with this notion, since the alternated square is nothing.1932, Harold Scott Macdonald Coxeter, The densities of the regular polytopes, part 2, reprinted in 1995, F. Arthur Sherk, Peter Mcmullen, Anthony C. Thompson, Asia Ivić Weiss (editors)...

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