*Polynomial equations and convex polytopes, by Bernd Sturmfels, in American Mathematical Montly, vol. 105, no. 10 (December 1998), 907-922.*

Like a polyhedron, a polytope has flat sides but possibly in higher dimensions; a convex polytope can be described by linear inequalities.

http://www.jstor.org/stable/2589283?&Search=yes&searchText=polytopes&searchText=equations&searchText=convex&searchText=Polynomial&list=hide&searchUri=%2Faction%2FdoBasicSearch%3Ffilter%3Djid%253A10.2307%252Fj100069%26Query%3DPolynomial%2Bequations%2Band%2Bconvex%2Bpolytopes%26wc%3Don%26Search.x%3D0%26Search.y%3D0&prevSearch=&item=1&ttl=35&returnArticleService=showFullText