@misc{HenkAverkov, author = {Henk, Martin and Averkov, Gennadiy}, title = {Three-Dimensional Polyhedra Can Be Described by Three Polynomial Inequalities}, series = {Discrete \& computational geometry}, volume = {42}, journal = {Discrete \& computational geometry}, number = {2}, issn = {1432-0444}, doi = {10.1007/s00454-009-9183-1}, pages = {166 -- 186}, abstract = {Bosse et al. conjectured that for every natural number d≥2 and every d-dimensional polytope P in ℝ d , there exist d polynomials p 1(x),…,p d (x) satisfying P={x∈ℝ d :p 1(x)≥0,…,p d (x)≥0}. We show that every three-dimensional polyhedron can be described by three polynomial inequalities, which confirms the conjecture for the case d=3 but also provides an analogous statement for the case of unbounded polyhedra. The proof of our result is constructive.}, language = {en} }