The Cell Structures of Certain Lattices (1991)
| Citations: | 18 - 7 self |
BibTeX
@INPROCEEDINGS{Conway91thecell,
author = {J. H. Conway and N. J. A. Sloane},
title = {The Cell Structures of Certain Lattices},
booktitle = {},
year = {1991},
pages = {71--107},
publisher = {Springer-Verlag}
}
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Abstract
. The most important lattices in Euclidean space of dimension n 8 are the lattices A n (n ³ 2), D n (n ³ 4), E n (n = 6 , 7 , 8) and their duals. In this paper we determine the cell structures of all these lattices and their Voronoi and Delaunay polytopes in a uniform manner. The results for E 6 * and E 7 * simplify recent work of Worley, and also provide what may be new space-filling polytopes in dimensions 6 and 7. 1. Introduction The Coxeter-Dynkin diagrams of types A n , D n , E 6 , E 7 and E 8 arise in surprisingly different parts of mathematics -- see the discussions by Arnold [1] and Hazewinkel et al. [30]. In the present paper we study __________________ * This paper appeared in {\m Miscellanea mathematica}, P. Hilton, F. Hirzebruch, and R. Remmert, Eds., Springer-Verlag, NY, 1991, pp. 71--107. (**) From the English version Auto-da-Fe(Continuum, New York, p. 385) as translated by C. V. Wedgwood: "You have but to know an object by its proper name for it to lose its dange...
