The six-dimensional Delaunay polytopes
نویسنده
چکیده
Given a lattice L, a full dimensional polytope P is called a Delaunay polytope if the set of its vertices is S ∩ L with S being an empty sphere of the lattice. Extending our previous work [DD01] on the hypermetric cone HY P7, we classify the six-dimensional Delaunay polytopes according to their combinatorial type. The list of 6241 combinatorial types is obtained by a study of the set of faces of the polyhedral cone HY P7.
منابع مشابه
Lattice-Free Polytopes and Their Diameter
A convex polytope in real Euclidean space is lattice-free if it intersects some lattice in space exactly in its vertex set. Lattice-free polytopes form a large and computationally hard class, and arise in many combinatorial and algorithmic contexts. In this article, aane and combinatorial properties of such polytopes are studied. First, bounds on some invariants, such as the diameter and layer-...
متن کامل0 Quadratic forms of rank 1 , closed zones and laminae
For a given lattice, we establish an equivalence involving a closed zone of the corresponding Voronoi polytope, a lamina hyperplane of the corresponding Delaunay partition and a quadratic form of rank 1 being an extreme ray of the corresponding L-type domain. 1991 Mathematics Subject classification: primary 52C07; secondary 11H55 An n-dimensional lattice determines two normal partitions of the ...
متن کاملNeighborly inscribed polytopes and Delaunay triangulations
We prove that there are superexponentially many combinatorially distinct d-dimensional neighborly Delaunay triangulations on n points. These are the first examples of neighborly Delaunay triangulations that cannot be obtained via a stereographic projection of an inscribed cyclic polytope, and provide the current best lower bound for the number of combinatorial types of Delaunay triangulations. ...
متن کاملDelaunay polytopes of cut lattices
We continue 3], the study of the lattice L n generated by cuts of the complete graph on a set V n of n vertices. The lattice L n spans an N = ? n 2-dimensional space of all functions deened on a set V 2 n of all unordered pairs of the set V n. We prove that the cut polytope, i.e. the convex hull of all cuts, is an asymmetric Delaunay polytope of L n. Symmetric Delaunay polytopes of a lattice L ...
متن کاملMany neighborly inscribed polytopes and Delaunay triangulations
We present a very simple explicit technique to generate a large family of point configurations with neighborly Delaunay triangulations. This proves that there are superexponentially many combinatorially distinct neighborly d-polytopes with n vertices that admit realizations inscribed on the sphere. These are the first examples of inscribable neighborly polytopes that are not cyclic polytopes, a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 25 شماره
صفحات -
تاریخ انتشار 2004