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A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the ''n''-dimensional space R''n''.〔 Some authors use the terms "convex polytope" and "convex polyhedron" interchangeably, while others prefer to draw a distinction between the notions of a polyhedron and a polytope. In addition, some texts require a polytope to be a bounded set, while others〔''Mathematical Programming'', by Melvyn W. Jeter (1986) ISBN 0-8247-7478-7, (p. 68 )〕 (including this article) allow polytopes to be unbounded. The terms "bounded/unbounded convex polytope" will be used below whenever the boundedness is critical to the discussed issue. Yet other texts treat a convex ''n''-polytope as a surface or (''n''-1)-manifold. Convex polytopes play an important role both in various branches of mathematics and in applied areas, most notably in linear programming. A comprehensive and influential book in the subject, called ''Convex Polytopes'', was published in 1967 by Branko Grünbaum. In 2003 the 2nd edition of the book was published, with significant additional material contributed by new writers.〔 In Grünbaum's book, and in some other texts in discrete geometry, convex polytopes are often simply called "polytopes". Grünbaum points out that this is solely to avoid the endless repetition of the word "convex", and that the discussion should throughout be understood as applying only to the convex variety. A polytope is called ''full-dimensional'' if it is an ''n''-dimensional object in R''n''. ==Examples== *Many examples of bounded convex polytopes can be found in the article "polyhedron". *In the 2-dimensional case the full-dimensional examples are a half-plane, a strip between two parallel lines, an angle shape (the intersection of two non-parallel half-planes), a shape defined by a convex polygonal chain with two rays attached to its ends, and a convex polygon. *Special cases of an unbounded convex polytope are a slab between two parallel hyperplanes, a wedge defined by two non-parallel half-spaces, a polyhedral cylinder (infinite prism), and a polyhedral cone (infinite cone) defined by three or more half-spaces passing through a common point. 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 polytope」の詳細全文を読む スポンサード リンク
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