Naslov
Perfect but not generating Delaunay polytopes

Autori
Dutour Sikiric, Mathieu ; Rybnikov, Konstantin

Izvornik
Symmetry: culture and science (0865-4824) 22 (2011); 317-325

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

Ključne riječi
Delaunay polytopes ; rigidity

Sažetak
In his seminal 1951 paper ``Extreme forms" Coxeter observed that for n>=9 one can add vectors to the perfect lattice A_9 so that the resulting perfect lattice, called A_9^2 by Coxeter, has exactly the same set of minimal vectors. An inhomogeneous analog of the notion of perfect lattice is that of a lattice with a perfect Delaunay polytope: the vertices of a perfect Delaunay polytope are the analogs of minimal vectors in a perfect lattice. We find a new infinite series P(n, s) for s>=2 and n+1>=4 of n-dimensional perfect Delaunay polytopes. A remarkable property of this series is that for certain values of s and all n>=13 one can add points to the integer affine span of P(n, s) in such a way that P(n, s) remains a perfect Delaunay polytope in the new lattice. Thus, we have constructed an inhomogeneous analog of the remarkable relationship between A_9 and A_9^2.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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