On some recent results in the metric theory of polyhedra (Q2707500)

This paper is a survey without proofs about several results concerning the metric structure of polyhedra in 3-space. The Burago-Zalgaller theorem on isometric embeddings of polyhedral 2-manifolds into 3-space provides a polyhedral analogue of the Nash-Kuiper embedding theorem. Furthermore, rigidity theorems for polyhedra are discussed, including volumes of polyhedra and the bellows conjecture which states that the volume of flexible polyhedra should be invariant during the flexing. The author describes his solution to the bellows conjecture in form of a sketch of a proof, for the details see Discrete Comput. Geom. 20, No. 4, 405-425 (1998; Zbl 0922.52006).NEWLINENEWLINEFor the entire collection see [Zbl 0948.00038].