The Contact Polytope of the Leech Lattice
نویسندگان
چکیده
The contact polytope of a lattice is the convex hull of its shortest vectors. In this paper we classify the facets of the contact polytope of the Leech lattice up to symmetry. There are 1,197,362,269,604,214,277,200 many facets in 232 orbits.
منابع مشابه
گزارش یک بیمار مبتلا به خونریزی از چشم به دنبال آلودگی با زالو
A leech attachment in the eye is very rare, yet leeches usually attach themselves to the throat, nasal mucus, esophagus, pharynx, rectum, and vagina. A leech can cause epistaxis, haematemesis, hemoptysis rectal and vaginal hemorrhage. In this article, a case of the eye contact to leech is reported. A seven year old boy with eye hemorrhage, who suffered from an attached leech in the limbus of th...
متن کاملExamples of Non-symmetric Kähler-einstein Toric Fano Manifolds
Let us first recall our setting. In the toric case, there is a correspondence between n-dimensional nonsingular Fano varieties and ndimensional Fano polytopes, where the Fano varieties are biregular isomorphic if and only if the corresponding Fano polytopes are unimodularly equivalent. Here, given a lattice N of rank n, a Fano polytope Q ⊆ NR := N ⊗Z R is given as a lattice polytope containing ...
متن کاملThe E 8 - lattice , the Leech lattice and beyond
In this elementary talk, we introduce basics about rational lattices and give examples. Some lattices are really good ones, notably the E8-lattice in dimension 8 and the Leech lattice in dimension 24. Both have remarkable finite isometry groups and give sphere packings of remarkably high minimum norms and high packing densities. Generalizations to higher dimensions have been considered, for exa...
متن کاملLocal Covering Optimality of Lattices : Leech Lattice versus Root Lattice E 8
The Leech lattice is the exceptional lattice in dimension 24. Soon after its discovery by Leech [9], it was conjectured that it is extremal for several geometric problems in R: the kissing number problem, the sphere packing problem, and the sphere covering problem. In 1979, Odlyzko and Sloane and independently Levenshtein solved the kissing number problem in dimension 24 by showing that the Lee...
متن کاملFour different types of a single drop dripping down a hole under gravity by lattice Boltzmann method
In this paper the dynamic of a droplet on a surface with a hole is investigated under gravitational effect by using lattice Boltzmann method. Incompressible two-phase flow with high density ratio proposed by Lee is considered. Cahn’s theory is used to observe the wettability of the surface in contact with liquid and gas phases. Several parameters such as contact angle, surface tension and gravi...
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:
- Discrete & Computational Geometry
دوره 44 شماره
صفحات -
تاریخ انتشار 2010