Octeractic honeycomb

The octeractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 8-space.

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

There are many different Wythoff constructions of this honeycomb. The most symmetric form is regular, with Schläfli symbol {4,3⁶,4}. Another form has two alternating hypercube facets (like a checkerboard) with Schläfli symbol {4,3⁵,3^1,1}. The lowest symmetry Wythoff construction has 256 types of facets around each vertex and a prismatic product Schläfli symbol {∞}⁸.

ee also

*Tesseractic honeycomb
*Penteractic honeycomb
*Hexeractic honeycomb
*Hepteractic 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