24-cell honeycomb

In four-dimensional Euclidean geometry, the 24-cell honeycomb, or icositetrachoric honeycomb is a regular space-filling tessellation (or honeycomb) of 4-dimensional Euclidean space by regular 24-cells. It can be represented by Schläfli symbol {3,4,3,3}.

24-cell honeycomb
A 24-cell and first layer of its adjacent 4-faces.
Type	Regular 4-honeycomb Uniform 4-honeycomb
Schläfli symbol	{3,4,3,3} r{3,3,4,3} 2r{4,3,3,4} 2r{4,3,31,1} {31,1,1,1}
Coxeter-Dynkin diagrams
4-face type	{3,4,3}
Cell type	{3,4}
Face type	{3}
Edge figure	{3,3}
Vertex figure	{4,3,3}
Dual	{3,3,4,3}
Coxeter groups	${\displaystyle {\tilde {F}}_{4}}$, [3,4,3,3] ${\displaystyle {\tilde {C}}_{4}}$, [4,3,3,4] ${\displaystyle {\tilde {B}}_{4}}$, [4,3,31,1] ${\displaystyle {\tilde {D}}_{4}}$, [31,1,1,1]
Properties	regular

The dual tessellation by regular 16-cell honeycomb has Schläfli symbol {3,3,4,3}. Together with the tesseractic honeycomb (or 4-cubic honeycomb) these are the only regular tessellations of Euclidean 4-space.