6-cubic honeycomb

The 6-cubic honeycomb or hexeractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 6-space.

6-cubic honeycomb
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Type	Regular 6-honeycomb Uniform 6-honeycomb
Family	Hypercube honeycomb
Schläfli symbol	{4,34,4} {4,33,31,1}
Coxeter-Dynkin diagrams
6-face type	{4,34}
5-face type	{4,33}
4-face type	{4,3,3}
Cell type	{4,3}
Face type	{4}
Face figure	{4,3} (octahedron)
Edge figure	8 {4,3,3} (16-cell)
Vertex figure	64 {4,34} (6-orthoplex)
Coxeter group	${\displaystyle {\tilde {C}}_{6}}$, [4,34,4] ${\displaystyle {\tilde {B}}_{6}}$, [4,33,31,1]
Dual	self-dual
Properties	vertex-transitive, edge-transitive, face-transitive, cell-transitive

It is analogous to the square tiling of the plane and to the cubic honeycomb of 3-space.