symmetry vs uniformity

symmetry

noun
  • The satisfying arrangement of a balanced distribution of the elements of a whole. 

  • Exact correspondence on either side of a dividing line, plane, center or axis. 

uniformity

noun
  • A collection of identical things 

  • The absence of alternatives or diversity; sameness. 

  • The state of being uniform, alike and lacking variety. 

How often have the words symmetry and uniformity occurred in a corpus of books? (source: Google Ngram Viewer )