关于三维Dirichlet立体面III的刻面数：全立方群
On the Number of Facets of Three-Dimensional Dirichlet Stereohedra III: Full Cubic Groups
摘要：
我们感兴趣的是三维晶体群的狄利克雷立体面所能具有的最大可能的刻面数。非三次群的问题在以前的文章中已经被D。Bochis和第二作者（离散计算。25：3（2001），419-444，and Beitr.代数几何，47：1（2006），89-120）。本文讨论的是“满"立方群，而”四分之一"立方群则留待以后的文章讨论。这里，“全"和”四分之一"是指最近由Conway、Delgado-Friedrichs、Huson和Thurston对三维晶体群的分类（math.MG/9911185，Beitr. 42.2（2001），475-507）。本文的主要结果是：27个完全群中任何一个的Dirichlet立体面都不能有多于25个的刻面。我们还发现这些群体之一的立体面与17方面。
英文摘要：
We are interested in the maximum possible number of facets that Dirichlet stereohedra for three-dimensional crystallographic groups can have. The problem for non-cubic groups was studied in previous papers by D. Bochis and the second author (Discrete Comput. Geom. 25:3 (2001), 419-444, and Beitr. Algebra Geom., 47:1 (2006), 89-120). This paper deals with ''full'' cubic groups, while ''quarter'' cubic groups are left for a subsequent paper. Here, ''full'' and ''quarter'' refers to the recent classification of three-dimensional crystallographic groups by Conway, Delgado-Friedrichs, Huson and Thurston (math.MG/9911185, Beitr. Algebra Geom. 42.2 (2001), 475-507). Our main result in this paper is that Dirichlet stereohedra for any of the 27 full groups cannot have more than 25 facets. We also find stereohedra with 17 facets for one of these groups.
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