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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, 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 diagrams.
The Coxeter symbol for these figures has the form ki,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 ki,j is i,j, and each of its facets are represented by subtracting one from one of the nonzero subscripts, i.e. ki − 1,j and ki,j − 1.
Rectified simplices are included in the list as limiting cases with k=0. Similarly 0i,j,k represents a bifurcated graph with a central node ringed.