Honeycomb (geometry)

In geometry, a honeycomb is the name given for a paving filling space by Polyèdre S, same manner that a Pavage fills a plan by polygons.

The term paving is also sometimes used for a three-dimensional paving, and honeycomb was defined to imply a solid paving more clearly. By generalization, the term is also used for pavings in higher dimensions. By clearness, George Olshevsky pled to limit the term honeycomb to three-dimensional pavings and to develop a systematic terminology for higher dimensions: tétracomb for pavings of space of dimension 4, pentacomb for pavings of space of dimension 5, and so on… (based on the Anglo-Saxon term honeycomb )

A honeycomb as paving filling space applies to pavings of hyperbolic space, such as the Petit hyperbolic dodecahedral honeycomb.

There exist 28 uniform convex honeycombs - the whole of the uniform honeycombs in the Euclidean three-dimensional space filled by the cells polyhedric convex uniforms.

Other honeycombs to uniform Cellule well-known include the rhombic dodecahedral Honeycomb, and the honeycomb rhombo-hexagonal Dodécaèdre.

The simplest honeycombs are layers piled up of prisms according to a paving of the plan. In particular, for each Parallelepiped, each copies can fill space, the cubic Honeycomb being a special regular form.

See too

regular Honeycombs

External bonds

Filling of space using only the rhombo-hexagonal dodecahedrons
Filling of space using only the rhombic dodecahedrons
Filling of space using only octahedral truncated the
Filling of the space using of the triangular, square and hexagonal prisms
Five polyhedrons filling space, Guy Inchbald
duaux honeycombs of Archimedes, Guy Inchbald
The Mathematical Gazette 80, November 1996, p.p. 466-475.

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