Editing Convex uniform honeycomb (section)

{{Short description|Spatial tiling of convex uniform polyhedra}}
[[File:Tetrahedral-octahedral honeycomb.png|320px|thumb|The ''alternated cubic honeycomb'' is one of 28 space-filling uniform tessellations in Euclidean 3-space, composed of alternating yellow [[tetrahedron|tetrahedra]] and red [[octahedron|octahedra]].]]
In [[geometry]], a '''convex uniform honeycomb''' is a [[uniform polytope|uniform]] [[tessellation]] which fills three-dimensional [[Euclidean space]] with non-overlapping [[convex polyhedron|convex]] [[uniform polyhedron|uniform polyhedral]] cells.

Twenty-eight such honeycombs are known:
* the familiar [[cubic honeycomb]] and 7 truncations thereof;
* the [[alternated cubic honeycomb]] and 4 truncations thereof;
* 10 prismatic forms based on the [[#Prismatic_stacks|uniform plane tilings]] (11 if including the cubic honeycomb);
* 5 modifications of some of the above by elongation and/or gyration.

They can be considered the three-dimensional analogue to the [[List of uniform planar tilings|uniform tilings of the plane]].

The [[Voronoi diagram]] of any [[Lattice (group)|lattice]] forms a convex uniform honeycomb in which the cells are [[zonohedra]].