Three-Dimensional Polyhedra Can Be Described by Three Polynomial Inequalities
نویسندگان
چکیده
Bosse et al. conjectured that for every natural number d ≥ 2 and every ddimensional polytope P in Rd there exist d polynomials p0(x), . . . , pd−1(x) satisfying P = { x ∈ Rd : p0(x) ≥ 0, . . . , pd−1(x) ≥ 0} . We show that for dimensions d ≤ 3 even every d-dimensional polyhedron can be described by d polynomial inequalities. The proof of our result is constructive. 2000 Mathematics Subject Classification. Primary: 14P05, 52B11, 14Q99; Secondary: 52A20
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عنوان ژورنال:
- Discrete & Computational Geometry
دوره 42 شماره
صفحات -
تاریخ انتشار 2009