Perfect Prismatoids are Lattice Delaunay Polytopes
| Autor: | M. A. Kozachok, A. N. Magazinov |
|---|---|
| Jazyk: | English<br />Russian |
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Моделирование и анализ информационных систем, Vol 21, Iss 4, Pp 47-53 (2014) |
| Druh dokumentu: | article |
| ISSN: | 1818-1015 2313-5417 |
| DOI: | 10.18255/1818-1015-2014-4-47-53 |
| Popis: | A perfect prismatoid is a convex polytope P such that for every its facet F there exists a supporting hyperplane α k F such that any vertex of P belongs to either F or α. Perfect prismatoids concern with Kalai conjecture, that any centrally symmetric dpolytope P has at least 3d non-empty faces and any polytope with exactly 3d non-empty faces is a Hanner polytope. Any Hanner polytope is a perfect prismatoid (but not vice versa). A 0/1-polytope is a convex hull of some vertices of the d-dimensional unit cube. We prove that every perfect prismatoid is affinely equivalent to some 0/1-polytope of the same dimension. (And therefore every perfect prismatoid is a lattice polytope.) Let Λ be a lattice in Rd and D be a polytope inscribed in a sphere B. Denote a boundary of B by ∂B and an interior of B by int B. The polytope D is a lattice Delaunay polytope if Λ∩int B = ∅ and D is a convex hull of Λ∩∂B. We prove that every perfect prismatoid is affinely equivalent to some lattice Delaunay polytope. |
| Databáze: | Directory of Open Access Journals |
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