|
In 6-dimensional geometry, the 122 polytope is a uniform polytope, constructed from the E6 group. It was first published in E. L. Elte's 1912 listing of semiregular polytopes, named as V72 (for its 72 vertices).〔Elte, 1912〕 Its Coxeter symbol is 122, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-node sequence. There are two rectifications of the 122, construcated by positions points on the elements of 122. The rectified 122 is constructed by points at the mid-edges of the 122. The birectified 122 is constructed by points at the triangle face centers of the 122. These polytopes are from a family of 39 convex uniform polytopes in 6-dimensions, made of uniform polytope facets and vertex figures, defined by all permutations of rings in this Coxeter-Dynkin diagram: . == 1_22 polytope == 25px |- |bgcolor=#e7dcc3|Faces||2160 25px |- |bgcolor=#e7dcc3|Edges||720 |- |bgcolor=#e7dcc3|Vertices||72 |- |bgcolor=#e7dcc3|Vertex figure||Birectified 5-simplex: 022 50px |- |bgcolor=#e7dcc3|Petrie polygon||Dodecagon |- |bgcolor=#e7dcc3|Coxeter group||E6, 3,32,2, order 103680 |- |bgcolor=#e7dcc3|Properties||convex, isotopic |} The 1_22 polytope contains 72 vertices, and 54 5-demicubic facets. It has a birectified 5-simplex vertex figure. Its 72 vertices represent the root vectors of the simple Lie group E6. 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「1 22 polytope」の詳細全文を読む スポンサード リンク
|
