In geometry, the 1<sub>52</sub> honeycomb is a uniform tessellation of 8-dimensional Euclidean space. It contains 1<sub>42</sub> and 1<sub>51</sub> facets, in a birectified 8-simplex vertex figure. It is the final figure in the 1<sub>k2</sub> polytope 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 end of the 2-length branch leaves the 8-demicube, 1<sub>51</sub>.
Removing the node on the end of the 5-length branch leaves the 1<sub>42</sub>.
The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the birectified 8-simplex, 0<sub>52</sub>.