Taxonomy of lattice reduction

Several attributions exist for the reduced cells of lattices and for the reduction processes to produce them. The actual origins of the terms are compared and a taxonomy created. The terms ``Niggli reduction", ``Niggli cell", ``Delaunay reduction", and ``Delaunay cell" most accurately describe the crystallographic usages of reduced cells and reduction methods. An alternative spelling of Boris Delaunay's name, adopted by him later in life, is Delone.