An algorithm for finding conditions of existence and constructing a polyhedron with prescribed face directions and face perimeters (Q1357973)

This paper contains an algorithm for constructing a convex 3-polytope with prescribed facet normals and facet perimeters. Of course, such construction is not always possible, the author discusses necessary and sufficient conditions to be imposed on the perimeters and facet normals for the existence of the polytope. The paper continues work by \textit{A. D. Alexandrov} [see `Konvexe Polyeder', Berlin, Akademie-Verlag (1958; Zbl 0079.16303)]. Using basic linear algebra, the values of the edge lengths of the polytope are expressed as linear combinations of the perimeters.