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Gosset–Elte Figures
In geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular polytopes, regular, generated by a Wythoff construction with mirrors all related by order-2 and order-3 dihedral angles. They can be seen as ''one-end-ringed'' Coxeter–Dynkin diagram#Finite Coxeter groups, Coxeter–Dynkin diagrams. The Coxeter symbol for these figures has the form ''k''''i,j'', where each letter represents a length of order-3 branches on a Coxeter–Dynkin diagram with a single ring on the end node of a ''k'' length sequence of branches. The vertex figure of ''k''''i,j'' is (''k'' − 1)''i,j'', and each of its facets are represented by subtracting one from one of the nonzero subscripts, i.e. ''k''''i'' − 1,''j'' and ''k''''i'',''j'' − 1. Rectified simplex, simplices are included in the list as limiting cases with ''k''=0. Similarly ''0''''i,j,k'' represents a bifurcate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1 42 Polytope
In 8-dimensional geometry, the 142 is a uniform 8-polytope, constructed within the symmetry of the E8 (mathematics), E8 group. Its Coxeter symbol is 142, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-node sequences. The rectified 142 is constructed by points at the mid-edges of the 142 and is the same as the birectified 241, and the quadrirectified 421. These polytopes are part of a family of 255 (28 − 1) convex uniform polytopes in 8 dimensions, made of uniform polytope facets and vertex figures, defined by all non-empty combinations of rings in this Coxeter-Dynkin diagram: . 142 polytope The 142 is composed of 2400 facets: 240 Gosset 1 32 polytope, 132 polytopes, and 2160 7-demicubes (141). Its vertex figure is a birectified 7-simplex. This polytope, along with the demiocteract, can Honeycomb (geometry), tessellate 8-dimensional space, represented by the symbol 152, and Coxeter-Dynkin diagram: . Alternate name ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
