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|- |bgcolor=#e7dcc3|Coxeter-Dynkin diagram |colspan=2| |- |bgcolor=#e7dcc3|Cells |10 |5 5 ''3.3.3.3'' |- |bgcolor=#e7dcc3|Faces |colspan=2|30 |- |bgcolor=#e7dcc3|Edges |colspan=2|30 |- |bgcolor=#e7dcc3|Vertices |colspan=2|10 |- |bgcolor=#e7dcc3|Vertex figure |colspan=2| Triangular prism |- |bgcolor=#e7dcc3|Symmetry group |colspan=2|A4, (), order 120 |- |bgcolor=#e7dcc3|Petrie Polygon |colspan=2|Pentagon |- |bgcolor=#e7dcc3|Properties |colspan=2|convex, isogonal, isotoxal |- |bgcolor=#e7dcc3|Uniform index |colspan=2|''1'' 2 ''3'' |} In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells. Each edge has one tetrahedron and two octahedra. Each vertex has two tetrahedra and three octahedra. In total it has 30 triangle faces, 30 edges, and 10 vertices. Each vertex is surrounded by 3 octahedra and 2 tetrahedra; the vertex figure is a triangular prism. The vertex figure of the ''rectified 5-cell'' is a uniform triangular prism, formed by three octahedra around the sides, and two tetrahedra on the opposite ends.〔Conway, 2008〕 == Structure== Together with the simplex and 24-cell, this shape and its dual (a polytope with ten vertices and ten triangular bipyramid facets) was one of the first 2-simple 2-simplicial 4-polytopes known. This means that all of its two-dimensional faces, and all of the two-dimensional faces of its dual, are triangles. In 1997, Tom Braden found another dual pair of examples, by gluing two rectified 5-cells together; since then, infinitely many 2-simple 2-simplicial polytopes have been constructed.〔.〕〔.〕 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「Rectified 5-cell」の詳細全文を読む スポンサード リンク
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