• An (m,s)-super-metric d is a function defined over all (m+1)-uples of {1,...,n} such that
• d(x_1,....,x_[m+1]) is invariant by permutation of the x_i
• d(x_1,....,x_[m+1])=0 if two x_i are identical
• d(x_1,....,x_[m+1])>=0
• sd(x_1,....,x_[m+1])<=sum_{i=1}^{m+1} d(x_1,....,x_[i-1},x_[i+1],...,x_[m+1])
• The (m,s)-super-metric cone SMET^[m,s]_n is the polyhedral cone of all (m,s)-super-metrics
• The (m,s)-super-cut cone SCUT^[m,s]_n is the positive span of all (0,1)-valued extreme rays of SMET^[m,s]_n

SMET^[2,2]_5

dimension	10
group	Sym(5)
extreme rays	132 in 6 orbits
facets	20 in one orbit

see files 22SMET5.tex and 22SMET5.ps for details

SCUT^[2,2]_5

dimension	10
group	Sym(5)
extreme rays	20 in two orbits
facets	220 in six orbits

see files 22BRO5.tex and 22BRO5.ps for details

SMET^{3,3/2}_6

dimension	15
group	Sym(6)
extreme rays	331989 in 596 orbits
facets	45 in two orbits

see files 32SMET6.tex and 32SMET6.ps for details

SCUT^[3,2]_6
(the description is conjectured to be complete)

dimension	15
group	Sym(6)
extreme rays	247 in five orbits
facets	866745 in  1345 orbits

see files List1345_32SCUT6 for details

SMET^[3,5/2]_6

dimension	15
group	Sym(6)
extreme rays	85504 in 201 orbits
facets	45 in two orbits

see files 33SMET6.tex and 33SMET6.ps for details

SCUT^[3,3]_6

dimension	15
group	Sym(6)
extreme rays	21 in 2 orbits
facets	150 in 3 orbits

see files 33BRO6.tex and 33BRO6.ps for details

SMET^[4,2]_7

dimension	21
group	Sym(7)
extreme rays	2561166 in 661 orbits
facets	63 in two orbits

see files List661_42SMET7 for details

SMET^[4,3]_7

dimension	21
group	Sym(7)
extreme rays	838729 in 274 orbits
facets	63 in two orbits

see files List274_43SMET7 for details

see files 44SMET7.tex and 44SMET7.ps for details

SCUT^[4,4]_7

dimension	21
group	Sym(7)
extreme rays	112 in two orbits
facets	148554 in 114 orbits

see files List114_44SCUT7 for details

SMET^[5,2]_8

dimension	28
group	Sym(8)
extreme rays	at least 222891598 in at least 6228 orbits
facets	84 in two orbits

see files List30827_22SMET6 for details

SCUT^[2,2]_6

dimension	20
group	Sym(6)
extreme rays	96 in three orbits
facets	at least 243692840 in at least 341551 orbits