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.

Construction

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. Removing the node on the end of the 5-length branch leaves the 241. The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the 8-demicube, 151. The edge figure is the vertex figure of the vertex figure. This makes the rectified 7-simplex, 051.

Related polytopes and honeycombs