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|- |bgcolor=#e7dcc3|Coxeter diagram|| |- |bgcolor=#e7dcc3|Cells||pq digonal disphenoids |- |bgcolor=#e7dcc3|Faces||2pq triangles |- |bgcolor=#e7dcc3|Edges||pq+p+q |- |bgcolor=#e7dcc3|Vertices||p+q |- |bgcolor=#e7dcc3|Vertex figures||p-gonal bipyramid q-gonal bipyramid |- |bgcolor=#e7dcc3|Symmetry||(), order 4pq |- |bgcolor=#e7dcc3|Dual||p-q duoprism |- |bgcolor=#e7dcc3|Properties||convex, facet-transitive |- |colspan=2| |- |bgcolor=#e7dcc3 colspan=2 align=center|Set of dual uniform p-p duopyramids |- |bgcolor=#e7dcc3|Schläfli symbol|| + = 2 |- |bgcolor=#e7dcc3|Coxeter diagram|| |- |bgcolor=#e7dcc3|Cells||p2 tetragonal disphenoids |- |bgcolor=#e7dcc3|Faces||2p2 triangles |- |bgcolor=#e7dcc3|Edges||p2+2p |- |bgcolor=#e7dcc3|Vertices||2p |- |bgcolor=#e7dcc3|Vertex figure||p-gonal bipyramid |- |bgcolor=#e7dcc3|Symmetry|| = (), order 8p2 |- |bgcolor=#e7dcc3|Dual||p-p duoprism |- |bgcolor=#e7dcc3|Properties||convex, facet-transitive |} In geometry of 4 dimensions or higher, a duopyramid is a dual polytope of a duoprism. As a dual uniform polychoron, it is called a ''p''-''q'' duopyramid with a composite Schläfli symbol + , and Coxeter-Dynkin diagram . The regular 16-cell can be seen as a 4,4-duopyramid, , symmetry , order 128. A ''p-q dupyramid'' has Coxeter group symmetry (), order 4pq. When ''p'' and ''q'' are identical, the symmetry is doubled as , order ''8p2''. Edges exist on all pairs of vertices between the p-gon and q-gon. The 1-skeleton of a p-q duopyramid represents edges of each p and q polygon and ''pq'' complete bipartite graph between them. == Geometry== It can be seen as two regular planar polygons of ''p'' and ''q'' sides with the same center and orthogonal orientations in 4 dimensions. Along with the ''p'' and ''q'' edges of the two polygons, all permutation of points in one polygon to the other form edges. All faces are triangular, representing one edge of one polygon connected to one point of in the other polygon. The ''p'' and ''q'' sided polygons are ''hollow'', passing through the polytope center and don't define faces. Cells are tetrahedra constructed as all permutations of edge pairs between each polygon. It can be considered in analogy the relation of the 3D prisms and their dual bipyramids with Schläfli symbol + , and a rhombus in 2D as + . A bipyramid can be seen as a 3D degenerated duopyramid, by adding an edge across the digon on the inner axis, and adding intersecting interior triangles and tetrahedra connecting that new edge to p-gon vertices and edges. Other nonuniform polychora can be called duopyramids by the same construction, as two orthogonal and co-centered polygons, connected with edges with all combinations of vertex pairs between the polygons. The symmetry will be the product of the symmetry of the two polygons. So a ''rectangle-rectangle duopyramid'' would be topologically identical to the uniform ''4,4-duopyramid'', but a lower symmetry (), order 16, possibly doubled to 32 if the two rectangles are identical. 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「Duopyramid」の詳細全文を読む スポンサード リンク
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