User joseph o'rourke - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T13:53:20Z http://mathoverflow.net/feeds/user/5845 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/6690/what-is-known-about-polyhedra-nets-that-allow-overlapping/23509#23509 Answer by Joseph O'Rourke for What is known about polyhedra nets that allow overlapping? Joseph O'Rourke 2010-05-04T23:17:54Z 2010-05-04T23:17:54Z <p>I would like to point out a closely related question, which is described in our <a href="http://www.gfalop.org/" rel="nofollow">book</a> that Joe Malkevitch mentioned (p.308). We called it the <em>Fewest Nets</em> problem. What is the fewest number of non-overlapping nets into which you can partition the surface of a convex polyhedron, cutting along polyhedron edges? The answer might be 1. But our ignorance leaves us with just fractions of F, the number of faces of the polyhedon. The best fraction obtained to date (as far as I know) is (1/2)F.</p>