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In five-dimensional geometry, a rectified 5-orthoplex is a convex uniform 5-polytope, being a rectification of the regular 5-orthoplex. There are 5 degrees of rectifications for any 5-polytope, the zeroth here being the 5-orthoplex itself, and the 4th and last being the 5-cube. Vertices of the rectified 5-orthoplex are located at the edge-centers of the 5-orthoplex. Vertices of the birectified 5-orthoplex are located in the triangular face centers of the 5-orthoplex. == Rectified 5-orthoplex== 32 t1 |- |bgcolor=#e7dcc3|Cells||240 total: 80 160 |- |bgcolor=#e7dcc3|Faces||400 total: 80+320 |- |bgcolor=#e7dcc3|Edges||240 |- |bgcolor=#e7dcc3|Vertices||40 |- |bgcolor=#e7dcc3|Vertex figure||40px Octahedral prism |- |bgcolor=#e7dcc3|Petrie polygon||Decagon |- |bgcolor=#e7dcc3|Coxeter groups||BC5, () D5, () |- |bgcolor=#e7dcc3|Properties||convex |} Its 40 vertices represent the root vectors of the simple Lie group D5. The vertices can be seen in 3 hyperplanes, with the 10 vertices rectified 5-cells cells on opposite sides, and 20 vertices of a runcinated 5-cell passing through the center. When combined with the 10 vertices of the 5-orthoplex, these vertices represent the 50 root vectors of the B5 and C5 simple Lie groups. E. L. Elte identified it in 1912 as a semiregular polytope, identifying it as Cr51 as a first rectification of a 5-dimensional cross polytope. 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-orthoplexes」の詳細全文を読む スポンサード リンク
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