In four-dimensional Euclidean geometry, the **16-cell honeycomb** is one of the three regular space-filling tessellations (or honeycombs) in Euclidean 4-space. The other two are its dual the 24-cell honeycomb, and the tesseractic honeycomb. This honeycomb is constructed from 16-cell facets, three around every face. It has a 24-cell vertex figure.

This vertex arrangement or lattice is called the B_{4}, D_{4}, or F_{4} lattice.

Hexadecachoric tetracomb/honeycomb
Demitesseractic tetracomb/honeycomb
As a regular honeycomb, {3,3,4,3}, it has a 2-dimensional analogue, {3,6}, and as an alternated form (the **demitesseractic honeycomb**, h{4,3,3,4}) it is related to the alternated cubic honeycomb.

Vertices can be placed at all integer coordinates (i,j,k,l), such that the sum of the coordinates is even.

The vertex arrangement of the 16-cell honeycomb is called the D_{4} lattice or F_{4} lattice. The vertices of this lattice are the centers of the 3-spheres in the densest known packing of equal spheres in 4-space; its kissing number is 24, which is also the same as the kissing number in **R**^{4}, as proved by Oleg Musin in 2003.

The D+

4 lattice (also called D2

4) can be constructed by the union of two D_{4} lattices, and is identical to the tesseractic honeycomb:

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This packing is only a lattice for even dimensions. The kissing number is 2^{3} = 8, (2^{n – 1} for *n* < 8, 240 for *n* = 8, and 2*n*(*n* – 1) for *n* > 8).

The D*

4 lattice (also called D4

4 and C2

4) can be constructed by the union of all four D_{4} lattices, but it is identical to the *D*_{4} lattice: It is also the 4-dimensional body centered cubic, the union of two 4-cube honeycombs in dual positions.

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The kissing number of the D*

4 lattice (and D_{4} lattice) is 24 and its Voronoi tessellation is a 24-cell honeycomb, , containing all rectified 16-cells (24-cell) Voronoi cells, or .

There are three different symmetry constructions of this tessellation. Each symmetry can be represented by different arrangements of colored 16-cell facets.

It is related to the regular hyperbolic 5-space 5-orthoplex honeycomb, {3,3,3,4,3}, with 5-orthoplex facets, the regular 4-polytope 24-cell, {3,4,3} with octahedral (3-orthoplex) cell, and cube {4,3}, with (2-orthoplex) square faces.

This honeycomb is one of 20 uniform honeycombs constructed by the
D
~
5
Coxeter group, all but 3 repeated in other families by extended symmetry, seen in the graph symmetry of rings in the Coxeter–Dynkin diagrams. The 20 permutations are listed with its highest extended symmetry relation: