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On a class of polyhedra. (Russian) Zbl 0673.52007

Let P be a fixed convex polygon in a plane H. The author characterizes the set of all convex polytopes A in the positive halfspace \(H^+\) with bases P and \(P'\), where \(P'\) is any translate of P in \(H'\) and all A- faces \(F\neq P\), \(P'\) are parallelograms.
Reviewer’s remark: The author’s theorem is trivial and holds in higher dimensions too: A convex d-polytope A is such a “generalized prism” with a fixed (d-1)-polytope P as basis if and only if A is the Minkowski- sum \(A-P+I_ 1+...+I_ n\) of P and segments \(I_ k\) with distinct directions non parallel to the affine hull of P. The directions of the segments \(I_ k\) are edge-directions of the facets \(F\neq P,P'\) of A, which are generalized (d-1)-prisms.
Reviewer: E.Hertel

MSC:

52Bxx Polytopes and polyhedra
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