In geometry, the **1 _{52} honeycomb** is a uniform tessellation of 8-dimensional Euclidean space. It contains

**1**and

_{42}**1**facets, in a birectified 8-simplex vertex figure. It is the final figure in the 1

_{51}_{k2}polytope 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 end of the 2-length branch leaves the 8-demicube, 1_{51}.

Removing the node on the end of the 5-length branch leaves the 1_{42}.

The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the birectified 8-simplex, 0_{52}.

## References

1 52 honeycomb Wikipedia(Text) CC BY-SA