alternation

Etymology

Latin alternatio; compare French alternation. Morphologically alternate + -ion

noun

1. The reciprocal succession of (normally two) things in time or place; the act of following and being followed by turns; alternate succession, performance, or occurrence
   the alternation of day and night
   alternation of summer and winter
   alternation between night shifts and day shifts
   alternation of feelings between hope and fear
2. (religion) The response of the congregation speaking alternately with the minister.
   There are Anthems to be found amongst them , where every syllable has its just length ; each part of a sentence its proper pause : where the words are not confused by perplexing alternations, or rendered tedious by unnecessary repetitions 1795, William Mason, Essays, Historical and Critical, on English Church Music
3. (phonology) Ablaut.
4. (linguistics) A pattern by which more than one construct is possible, as with "Alice cooked Bob dinner" and "Alice cooked dinner for Bob".
   dative alternation; locative alternation
5. (logic) The "inclusive or" truth function.
6. (mathematics) A sequence that alternates between positive and negative values; sometimes incorrectly used to mean permutation.
7. (computing) A construct in a regular expression that can match any of several specified subexpressions.
8. (geometry) A type of partial truncation of a polygon, polyhedron or tiling in which alternate vertices are removed.
   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), Kaleidoscopes: Selected Writings of H. S. M. Coxeter, page 54, 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.