 
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,
