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We are interested in the maximum possible number of facets that Dirichletstereohedra for three-dimensional crystallographic groups can have. The problemfor non-cubic groups was studied in previous papers by D. Bochis and the secondauthor (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-dimensionalcrystallographic 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 27full groups cannot have more than 25 facets. We also find stereohedra with 17facets for one of these groups.Comment: 28 pages, 12 figures. Changes from v1: apart of some editing (mostly  at the end of the introduction) and addition of references, an appendix has  been added, which analyzes the case where the base point does not have  trivial stabilize

On the Number of Facets of Three-Dimensional Dirichlet Stereohedra III: Full Cubic Groups