Naslov
The seven Dimensional Perfect Delaunay Polytopes and Delaunay Simplices

Autori
Dutour Sikirić, Mathieu

Izvornik
Canadian journal of mathematics (0008-414X) 69 (2017); 1143-1168

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

Ključne riječi
Delaunay polytope, enumeration, polyhedral methods

Sažetak
For a lattice L of R^n, a sphere S(c, r) of center c and radius r is called empty if for any v∈L we have ∥v−c∥≥r. Then the set S(c, r)∩L is the vertex set of a Delaunay polytope P=conv(S(c, r)∩L). A Delaunay polytope is called perfect if any affine transformation ϕ such that ϕ(P) is a Delaunay polytope is necessarily an isometry of the space composed with an homothety. Perfect Delaunay polytopes are remarkable structure that exist only if n=1 or n≥6 and they have shown up recently in covering maxima studies. Here we give a general algorithm for their enumeration that relies on the Erdahl cone. We apply this algorithm in dimension 7 which allow us to find that there are only two perfect Delaunay polytopes: 321 which is a Delaunay polytope in the root lattice E7 and the Erdahl Rybnikov polytope. We then use this classification in order to get the list of all types Delaunay simplices in dimension 7 and found 11 types.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA