All the Facets of the Six Point Hamming Cone School of Computer Science Summary: All the Facets of the Six Point Hamming Cone David Avis Mutt School of Computer Science McGill University 805 Sherbrooke St. West Montreal, Quebec H3A 2K6 ABSTRACT A finite semimetric is L 1 - embeddable if it can be expressed as a non­ negative combination of Hamming semimetrics. The cone of such semimetrics is called the Hamming cone. A finite semimetric is called hypermetric if it satisfies the (2k + 1) - gonal inequalities which naturally generalize the triangle inequal­ ity. With the aid of a computer we show that a semimetric on six points is hyper­ metric if and only if it is L 1 - embeddable and give a complete list of the the facets of the six point Hamming cone. It is known that there are seven point hypermetrics that are not L 1 - embeddable. 1. Introduction For an integer n and a finite set X = {x 1 , . . . , x n }, let (X, d) be a semimetric space. In other words, Collections: Computer Technologies and Information Sciences