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## Perfect forms and perfect Delaunay

Dutour Sikirić, Mathieu
Perfect forms and perfect Delaunay // Ben Gurion University of the Negev
Ber Sheva, 2012. (predavanje, međunarodna recenzija, pp prezentacija, znanstveni)

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Naslov
Perfect forms and perfect Delaunay

Autori
Dutour Sikirić, Mathieu

Sažeci sa skupova, pp prezentacija, znanstveni

Izvornik
Ben Gurion University of the Negev / - , 2012

Skup
BGU Seminar on Algebraic Combinatorics

Mjesto i datum
Ber Sheva, 24.11.2012

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
polytopes; lattices; sphere packing problem; sphere covering problem.

Sažetak
A lattice packing is a family of non-overlapping balls whose center belongs to a lattice L. The density of a packing is the fraction of space occupied by them and the lattice packing problem is to find the lattice of maximum density. We will expose the theory of Voronoi for lattice packings, that is the notion of perfect form, Ryshkov polyhedron and Voronoi algorithm that allow to solve the lattice packing problem up to dimension 8. Along the way we will shortly introduce root lattices, the Leech lattice and the well rounded retract. Then we will consider the covering problem where one wants to cover the space by balls whose center belong to a lattice. We will shortly discussthe problem of minimizing the covering density and then we will remark that the root lattice E6 is actually a local maxima for the covering density. This allows us to introduce the Erdahl cone, the notion of perfect Delaunay polytopes and a Voronoi algorithm for their enumeration.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekti:
098-0982705-2707 - Matematičko modeliranje cirkulacije i satelitska detekcija graničnih procesa (Kuzmić, Milivoj, MZOS ) ( POIROT)

Ustanove:
Institut "Ruđer Bošković", Zagreb

Profili:

Mathieu Dutour Sikirić (autor)

#### Citiraj ovu publikaciju:

Dutour Sikirić, Mathieu
Perfect forms and perfect Delaunay // Ben Gurion University of the Negev
Ber Sheva, 2012. (predavanje, međunarodna recenzija, pp prezentacija, znanstveni)
Dutour Sikirić, M. (2012) Perfect forms and perfect Delaunay. U: Ben Gurion University of the Negev.
@article{article, author = {Dutour Sikiri\'{c}, Mathieu}, year = {2012}, keywords = {polytopes, lattices, sphere packing problem, sphere covering problem.}, title = {Perfect forms and perfect Delaunay}, keyword = {polytopes, lattices, sphere packing problem, sphere covering problem.}, publisherplace = {Ber Sheva} }
@article{article, author = {Dutour Sikiri\'{c}, Mathieu}, year = {2012}, keywords = {polytopes, lattices, sphere packing problem, sphere covering problem.}, title = {Perfect forms and perfect Delaunay}, keyword = {polytopes, lattices, sphere packing problem, sphere covering problem.}, publisherplace = {Ber Sheva} }

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