see page http://www.cas.mcmaster.ca/~deza/metric.html for the metric polytopes and cones

see page http://www.iwr.uni-heidelberg.de/groups/comopt/software/SMAPO/cut/cut.html for the cut polytopes

The metric cone MET_n is defined by the following n(n-1)(n-2)/2 triangle inequalities:

• x_{ij}+x_{jk}-x_{ik} >= 0       for all triples {i,j,k} of {1,...,n}

• Delta(S)ij=1, if i\in S and j\notin S
• Delta(S)ij=1, if i\notin S and j\in S
• Delta(S)ij=0, if i\notin S and j\notin S
• Delta(S)ij=0, if i\in S and j\in S

Here I give a list of metric cones. All computations were done using cdd and perl scripts.

see files CUT3.tex and CUT3.ps for details

see files CUT4.tex and CUT4.ps for details

see files CUT5.tex and CUT5.ps for details
 

The cone MET_5

dimension	10
group	Sym(5)
extreme rays	25 in three orbits
facets	30 in one orbit

see files MET5.tex and MET5.ps for details

see files CUT6.tex and CUT6.ps for details
 

The cone MET_6

dimension	15
group	Sym(6)
extreme rays	296 in seven orbits
facets	60 in one orbit

see files MET6.tex and MET6.ps for details

see files CUT7.tex and CUT7.ps for details

The cone MET_7

dimension	21
group	Sym(7)
extreme rays	55226 in 46 orbits
facets	105 in 1 orbits

see files MET7.tex and MET7.ps for details

The cone CUT_8

dimension	28
group	Sym(8)
extreme rays	127 in 4 orbits
facets	49604520 in 2169 orbits

see files List2169_CUT8 for details

The cone MET_8

dimension	28
group	Sym(8)
extreme rays	119269588 in 3918 orbits
facets	168 in one orbit

see files List3918_MET8 for details