Uniform 1 k2 polytope
Uniform 1k2 polytopes are a family of shapes in dimensions n = k + 4, built from the E_n Coxeter group. They get their name from the 1k2 Coxeter–Dynkin diagram, which has a single ring on the end of the 1‑node branch. They can also be described by the extended Schläfli symbol {3,3k,2}.
The family starts at six dimensions with 6‑polytopes, and can be traced back to include the 5‑dimensional demicube (the demipenteract) and the 4‑dimensional 5‑cell. Each member has facets that come from 1k−1,2 and from (n−1)‑demicubes. Its vertex figure is the {31,n−2,2} polytope, and it is a birectified n‑simplex, t2{3n}.
The sequence ends at k = 6 (n = 10), corresponding to an infinite tessellation of 9‑dimensional hyperbolic space.
The complete family of 1k2 polytopes are:
This page was last edited on 3 February 2026, at 19:56 (CET).