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.

Read more about Convex Uniform Honeycomb:  History, Compact Euclidean Uniform Tessellations (by Their Infinite Coxeter Group Families), Noncompact Forms, Hyperbolic Forms

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