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What (who) is 5-cubic honeycomb - definition
5-cubic honeycomb
TILING OF FIVE-DIMENSIONAL SPACE
Penteractic pentacomb; 5-cube honeycomb; Penteractic honeycomb; Tritruncated 5-cubic honeycomb
The 5-cubic honeycomb or penteractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 5-space. Four 5-cubes meet at each cubic cell, and it is more explicitly called an order-4 penteractic honeycomb.
Order-5 cubic honeycomb
![It is analogous to the 2D hyperbolic [[order-5 square tiling]], {4,5}](https://commons.wikimedia.org/wiki/Special:FilePath/H2-5-4-primal.svg?width=200 "It is analogous to the 2D hyperbolic [[order-5 square tiling]], {4,5}")
![It can be seen as analogous to the 2D hyperbolic [[tetrapentagonal tiling]], r{4,5} with square and pentagonal faces](https://commons.wikimedia.org/wiki/Special:FilePath/H2-5-4-rectified.svg?width=200 "It can be seen as analogous to the 2D hyperbolic [[tetrapentagonal tiling]], r{4,5} with square and pentagonal faces")
REGULAR TILING OF HYPERBOLIC 3-SPACE
Hyperbolic great cubic honeycomb; Alternated order-5 cubic honeycomb; Rectified order-5 cubic honeycomb; Omnitruncated order-5 cubic honeycomb; Runcitruncated order-5 cubic honeycomb; Cantitruncated order-5 cubic honeycomb; Cantellated order-5 cubic honeycomb; Runcinated order-5 cubic honeycomb; Truncated order-5 cubic honeycomb; Bitruncated order-5 cubic honeycomb; Runcicantic order-5 cubic honeycomb; Runcic order-5 cubic honeycomb; Cantic order-5 cubic honeycomb; Runcinated order-4 dodecahedral honeycomb; Omnitruncated order-4 dodecahedral honeycomb; Order-3-5 square honeycomb
In hyperbolic geometry, the order-5 cubic honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli symbol it has five cubes around each edge, and 20 cubes around each vertex.
Cubic honeycomb
ONLY REGULAR SPACE-FILLING TESSELLATION OF THE CUBE
Truncated cubic honeycomb; Rectified cubic honeycomb; Cantellated cubic honeycomb; Runcitruncated cubic honeycomb; Cantitruncated cubic honeycomb; Omnitruncated cubic honeycomb; Truncated square prismatic honeycomb; Snub square prismatic honeycomb; Runcinated cubic honeycomb; 3-cube honeycomb; Alternated cantitruncated cubic honeycomb; Regular cubic honeycomb; Runcicantellated cubic honeycomb; Runcinated cubic honycomb; D3 lattice; Snub rectified cubic honeycomb; Runcic cantitruncated cubic honeycomb; Alternated omnitruncated cubic honeycomb; Cubic cellulation; Rectified cubic cellulation; Truncated cubic cellulation; Cantellated cubic cellulation; Runcinated cubic cellulation; Cantitruncated cubic cellulation; Runcitruncated cubic cellulation; Omnitruncated cubic cellulation; Simo-square prismatic cellulation; Tomo-square prismatic cellulation; Quarter oblate octahedrille; Square quarter pyramidille; Triangular pyramidille; Order-3-4 square honeycomb; Cantic snub cubic honeycomb
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.
