LOW-DIMENSIONAL LATTICES .6. VORONOI REDUCTION OF 3-DIMENSIONAL LATTICES

被引：47

作者：

CONWAY, JH ^{[1
]}

SLOANE, NJA ^{[1
]}

机构：

[1] AT&T BELL LABS,MATH SCI RES CTR,MURRAY HILL,NJ 07974

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1992年 / 436卷 / 1896期

关键词：

D O I：

10.1098/rspa.1992.0004

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The aim of this paper is to describe how the Voronoi cell of a lattice changes as that lattice is continuously varied. The usual treatment is simplified by the introduction of new parameters called the vonorms and conorms of the lattice. The present paper deals with dimensions n less-than-or-equal-to 3: a sequel will treat four-dimensional lattices. An elegant algorithms is given for the Voronoi reduction of a three-dimensional lattice. leading to a new proof of Voronoi's theorem that every lattice of dimension n less-than-or-equal-to 3 is of the first kind, and of Fedorov's classification of the three-dimensional lattices into five types. There is a very simple formula for the determinant of a three-dimensional lattice in terms of its conorms.

引用

页码：55 / 68

页数：14

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