Naslov
The hypermetric cone on seven vertices

Autori
Deza, Michel ; Dutour, Mathieu

Izvornik
Experimental Mathematics (1058-6458) 12 (2003), 4; 433-440

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
polyhedral cone; Delaunay polytope; extremal property

Sažetak
The hypermetric cone HYPn is the set of vectors dij satisfying the hypermetric inequalities. A Delaunay polytope of a lattice is called extreme if the only affine bijective transformations of it into a Delaunay polytope, are the homotheties ; there is correspondence between such Delaunay polytopes and extreme rays of HYPn. We show that unique Delaunay polytopes of root lattices A1 and E6 are the only extreme Delaunay polytopes of dimension at most 6. We describe also the skeletons and adjacency properties of HYP7 and of its dual. The computational technique used is polyhedral, i.e. enumeration of extreme rays, using the program cdd, and group theory to reduce the size of the computations.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA