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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—Thomas Jefferson (1743–1826)