In 8-dimensional geometry, the 2<sub>51</sub> honeycomb is a space-filling uniform tessellation. It is composed of 2<sub>41</sub> polytope and 8-simplex facets arranged in an 8-demicube vertex figure. It is the final figure in the 2<sub>k1</sub> 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.
Removing the node on the end of the 5-length branch leaves the 2<sub>41</sub>.
The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the 8-demicube, 1<sub>51</sub>.
The edge figure is the vertex figure of the vertex figure. This makes the rectified 7-simplex, 0<sub>51</sub>.