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 ...
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