Six-point matching geometry
= Six-point matching geometry
The complete graph on six points has fifteen edges and fifteen perfect matchings. Its six one-factorizations organize a dual incidence geometry exchanging points with factorizations and edges with matchings. The classical names are <duads>, <synthemes> and <totals of synthemes>. This geometry supports <duad-syntheme duality on six points> and a construction of the <small Witt design>.