Difference between revisions of "Template:Honeycomb"
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A [[Honeycomb (geometry)|geometric honeycomb]] is a ''space-filling'' of [[polyhedron|polyhedral]] or higher-dimensional ''cells'', so that there are no gaps. It is an example of the more general mathematical ''tiling'' or ''[[tessellation]]'' in any number of dimensions. | A [[Honeycomb (geometry)|geometric honeycomb]] is a ''space-filling'' of [[polyhedron|polyhedral]] or higher-dimensional ''cells'', so that there are no gaps. It is an example of the more general mathematical ''tiling'' or ''[[tessellation]]'' in any number of dimensions. | ||
| − | Honeycombs are usually constructed in ordinary [[Euclidean geometry|Euclidean]] ("flat") space. They may also be constructed in [[non-Euclidean geometry|non-Euclidean spaces]], such as [[ | + | Honeycombs are usually constructed in ordinary [[Euclidean geometry|Euclidean]] ("flat") space, like the [[convex uniform honeycomb]]s. They may also be constructed in [[non-Euclidean geometry|non-Euclidean spaces]], such as [[Uniform honeycombs in hyperbolic space|hyperbolic uniform honeycombs]]. Any finite [[uniform polytope]] can be projected to its [[circumsphere]] to form a uniform honeycomb in spherical space. |
Revision as of 23:52, 20 May 2014
A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions.
Honeycombs are usually constructed in ordinary Euclidean ("flat") space, like the convex uniform honeycombs. They may also be constructed in non-Euclidean spaces, such as hyperbolic uniform honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical space.
