Uniform 2 k1 polytope | EPFL Graph Search

DISPLAYTITLE:Uniform 1 k2 polytope In geometry, 1k2 polytope is a uniform polytope in n-dimensions (n = k+4) constructed from the En Coxeter group. The family was named by their Coxeter symbol 1k2 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-node sequence. It can be named by an extended Schläfli symbol {3,3k,2}. The family starts uniquely as 6-polytopes, but can be extended backwards to include the 5-demicube (demipenteract) in 5-dimensions, and the 4-simplex (5-cell) in 4-dimensions.

DISPLAYTITLE:2 41 polytope In 8-dimensional geometry, the 241 is a uniform 8-polytope, constructed within the symmetry of the E8 group. Its Coxeter symbol is 241, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node sequences. The rectified 241 is constructed by points at the mid-edges of the 241. The birectified 241 is constructed by points at the triangle face centers of the 241, and is the same as the rectified 142.

DISPLAYTITLE:2 51 honeycomb In 8-dimensional geometry, the 251 honeycomb is a space-filling uniform tessellation. It is composed of 241 polytope and 8-simplex facets arranged in an 8-demicube vertex figure. It is the final figure in the 2k1 family. It is created by a Wythoff construction upon a set of 9 hyperplane mirrors in 8-dimensional space. The facet information can be extracted from its Coxeter-Dynkin diagram. Removing the node on the short branch leaves the 8-simplex.