Summary: In a series of recent papers [Econometrica 49, 1-32 (1981; Zbl 0446.90006); ibid. 49, 395-423 (1981; Zbl 0458.90008)] I have introduced a particular class of convex polyhedrain \(R^ n\), arising in the study of integer programming problems with n variables. In the present paper a detailed analysis of these polyhedra will be given for the case in which \(n=3\); the analysis is based on an unpublished theorem demonstrated several years ago by Roger Howe, which seems to have no immediate generalization to higher values of n.