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|- |bgcolor=#e7dcc3|Coxeter-Dynkin diagram|| |- |bgcolor=#e7dcc3|Cells||p,q-gonal prisms, q p-gonal prisms |- |bgcolor=#e7dcc3|Faces||pq squares, p q-gons, q p-gons |- |bgcolor=#e7dcc3|Edges||2pq |- |bgcolor=#e7dcc3|Vertices||pq |- |bgcolor=#e7dcc3|Vertex figure||100px disphenoid |- |bgcolor=#e7dcc3|Symmetry||(), order 4pq |- |bgcolor=#e7dcc3|Dual||p,q-duopyramid |- |bgcolor=#e7dcc3|Properties||convex, vertex-uniform |- |colspan=2| |- |bgcolor=#e7dcc3 colspan=2 align=center|Set of uniform p-p duoprisms |- |bgcolor=#e7dcc3|Type||Prismatic uniform 4-polytope |- |bgcolor=#e7dcc3|Schläfli symbol||× |- |bgcolor=#e7dcc3|Coxeter-Dynkin diagram|| |- |bgcolor=#e7dcc3|Cells||2p p-gonal prisms |- |bgcolor=#e7dcc3|Faces||p2 squares, 2p p-gons |- |bgcolor=#e7dcc3|Edges||2p2 |- |bgcolor=#e7dcc3|Vertices||p2 |- |bgcolor=#e7dcc3|Symmetry|| = (), order 8p2 |- |bgcolor=#e7dcc3|Dual||p-p duopyramid |- |bgcolor=#e7dcc3|Properties||convex, vertex-uniform, Facet-transitive |} In geometry of 4 dimensions or higher, a duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions or higher. The Cartesian product of an ''n''-polytope and an ''m''-polytope is an (''n''+''m'')-polytope, where ''n'' and ''m'' are 2 (polygon) or higher. The lowest-dimensional duoprisms exist in 4-dimensional space as 4-polytopes being the Cartesian product of two polygons in 2-dimensional Euclidean space. More precisely, it is the set of points: : where ''P1'' and ''P2'' are the sets of the points contained in the respective polygons. Such a duoprism is convex if both bases are convex, and is bounded by prismatic cells. ==Nomenclature== Four-dimensional duoprisms are considered to be prismatic 4-polytopes. A duoprism constructed from two regular polygons of the same edge length is a uniform duoprism. A duoprism made of ''n''-polygons and ''m''-polygons is named by prefixing 'duoprism' with the names of the base polygons, for example: a ''triangular-pentagonal duoprism'' is the Cartesian product of a triangle and a pentagon. An alternative, more concise way of specifying a particular duoprism is by prefixing with numbers denoting the base polygons, for example: 3,5-duoprism for the triangular-pentagonal duoprism. Other alternative names: * q-gonal-p-gonal prism * q-gonal-p-gonal double prism * q-gonal-p-gonal hyperprism The term ''duoprism'' is coined by George Olshevsky, shortened from ''double prism''. John Horton Conway proposed a similar name proprism for ''product prism'', a Cartesian product of two or more polytopes of dimension at least two. The duoprisms are proprisms formed from exactly two polytopes. 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「Duoprism」の詳細全文を読む スポンサード リンク
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