# 5-simplex honeycomb

In five-dimensional Euclidean geometry, the **5-simplex honeycomb** or **hexateric honeycomb** is a space-filling tessellation (or honeycomb or pentacomb). Each vertex is shared by 12 5-simplexes, 30 rectified 5-simplexes, and 20 birectified 5-simplexes. These facet types occur in proportions of 2:2:1 respectively in the whole honeycomb.

The A^{*}_{5} lattice (also called A^{6}_{5}) is the union of six A_{5} lattices, and is the dual vertex arrangement to the omnitruncated 5-simplex honeycomb, and therefore the Voronoi cell of this lattice is an omnitruncated 5-simplex.

The *5-simplex honeycomb* can be projected into the 3-dimensional cubic honeycomb by a geometric folding operation that maps two pairs of mirrors into each other, sharing the same vertex arrangement: