This page is critized as erronneous.
In an email to Ulf Rehmann, dated Apr 21, 2012, Branko Günbaum says:
... I am sorry to have to report that this is totally unacceptable. There is nothing "abstract" about the material described in the text, but there are quite horrendous errors. One of them is the assertion that "... any open subset of a Euclidean space is a polyhedron" -- this coming right after we are told that a polyhedron is the finite union of closed (actually compact) convex sets. Clearly, the writer had some other concepts in mind -- but it is hard to make local changes in a connected set of entries.
Polyhedron, abstract. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Polyhedron,_abstract&oldid=25367