The quasi-semi-metric cone QMET_n is defined by:

• the n(n-1)(n-2)oriented triangle inequalities: x_{ij}+x_{jk}-x_{ik} >= 0       for all triples {i,j,k} of {1,...,n}
• the n(n-1)non-negativity inequalities: x_{ij} >= 0       for all couples {i,j} of {1,...,n}

• Delta(S_1, ....., S_q)ij=1, if i\in S_h and j\in S_k with h< k
• Delta(S_1, ....., S_q)ij=0, otherwise

see files OMCUT3-QMET3.tex and OMCUT3-QMET3.ps for details

see files OMCUT4.tex and OMCUT4.ps for details

The cone QMET_4

dimension	12
group	Sym(4) x Z2
extreme rays	164 in ten orbits
facets	36 in two orbits

see files QMET4.tex and QMET4.ps for details

The cone QMET_5

dimension	20
group	Sym(5) x Z2
extreme rays	43590 in 229 orbits
facets	80 in 2 orbits

see files QMET5.tex and QMET5.ps for details

The cone QHYP_5

dimension	20
group	Sym(5)x Z2
extreme rays	78810 in 386 orbits
facets	90 in 3 orbits

see files qhyp5.tex and qhyp5.ps for details 

The cone QMET_6

dimension	20
group	Sym(6) x Z2
extreme rays	at least 492157440 in at least 343577 orbits
facets	150 in 2 orbits