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
Famous quotes containing the word uniform:
“The sugar maple is remarkable for its clean ankle. The groves of these trees looked like vast forest sheds, their branches stopping short at a uniform height, four or five feet from the ground, like eaves, as if they had been trimmed by art, so that you could look under and through the whole grove with its leafy canopy, as under a tent whose curtain is raised.”
—Henry David Thoreau (1817–1862)