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A convex lattice polytope (also called Z-polyhedron or Z-polytope) is a geometric object playing an important role in discrete geometry and combinatorial commutative algebra. It is a polytope in a Euclidean space Rn which is a convex hull of finitely many points in the integer lattice Zn ⊂ Rn. Such objects are prominently featured in the theory of toric varieties, where they correspond to polarized projective toric varieties. == Examples == * An ''n''-dimensional simplex Δ in Rn+1 is the convex hull of ''n''+1 points that do not lie on a single affine hyperplane. The simplex is a convex lattice polytope if (and only if) the vertices have integral coordinates. The corresponding toric variety is the ''n''-dimensional projective space Pn. * The unit cube in Rn, whose vertices are the ''2''n points all of whose coordinates are ''0'' or ''1'', is a convex lattice polytope. The corresponding toric variety is the Segre embedding of the ''n''-fold product of the projective line P1. * In the special case of two-dimensional convex lattice polytopes in R2, they are also known as convex lattice polygons. * In algebraic geometry, an important instance of lattice polytopes called the Newton polytopes are the convex hulls of the set which consists of all the exponent vectors appearing in a collection of monomials. For example, consider the polynomial of the form with has a lattice equal to the triangle : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「convex lattice polytope」の詳細全文を読む スポンサード リンク
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