Convex Uniform Honeycomb

In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.

Twenty-eight such honeycombs exist:

• the familiar cubic honeycomb and 7 truncations thereof;
• the alternated cubic honeycomb and 4 truncations thereof;
• 10 prismatic forms based on the 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 uniform tilings of the plane.