The structure of normal subsets of polyhedral cone The structure of normal convex subsets of polyhedral cone K in normalized space is in investigated. The normality of the subset Ω ⊂ K (in the sense of the cone K) is determined by the condition Ω − K ∩ K = Ω (a line over a set means taking a topological closure). The conical shell of finite number of rays mean the polyhedrons of the cone, which are extreme rays. The structure of normal sets were studied from the geometric point of view. It is shown that every normal subset Ω of a polyhedral cone can be divided into a sum of two subsets, one of which is a bounded normal subset (in the sense of some subcone in K) and the second-the subcone K contained in the set Ω (it is unbounded, if Ω is unbounded).