Penteractic honeycomb

The penteractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 5-space. Four penteracts meet at each cubic cell, and it is more explicitly called an "order-4 penteractic honeycomb".

It is an analog of the square tiling of the plane, the cubic honeycomb of 3-space, and the tesseractic honeycomb of 4-space.

It is also related to the regular hexeract which exists in 6-space with "3" penteracts on each cell. This could be considered as a tessellation on the 5-sphere, an "order-3 penteractic honeycomb", {4,3,3,3,3}.

ee also

*Tesseractic honeycomb
*Hexeractic honeycomb
*List of regular polytopes

References

* Coxeter, H.S.M. "Regular Polytopes", (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 p.296, Table II: Regular honeycombs