alikeness vs symmetry

alikeness

noun
  • The result or product of being alike. 

  • The state or quality of being alike. 

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. 

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