Cubic honeycomb
Only regular space-filling tessellation of the cube / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Snub square prismatic honeycomb?
Summarize this article for a 10 year old
The cubic honeycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb) in Euclidean 3-space made up of cubic cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its vertex figure is a regular octahedron. It is a self-dual tessellation with Schläfli symbol {4,3,4}. John Horton Conway called this honeycomb a cubille.
Cubic honeycomb | |
---|---|
Type | Regular honeycomb |
Family | Hypercube honeycomb |
Indexing[1] | J11,15, A1 W1, G22 |
Schläfli symbol | {4,3,4} |
Coxeter diagram | |
Cell type | {4,3} |
Face type | square {4} |
Vertex figure | octahedron |
Space group Fibrifold notation | Pm3m (221) 4−:2 |
Coxeter group | , [4,3,4] |
Dual | self-dual Cell: |
Properties | Vertex-transitive, regular |
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.