6-cubic honeycomb

6-cubic honeycomb
(no image)
Type Regular 6-space honeycomb
Family Hypercube honeycomb
Schläfli symbol {4,3,3,3,3,4}
{4,3,3,3,31,1}
Coxeter-Dynkin diagrams


6-face type {4,3,3,3,3}
5-face type {4,3,3,3}
4-face type {4,3,3}
Cell type {4,3}
Face type {4}
Face figure {4,3}
(octahedron)
Edge figure 8 {4,3,3}
(16-cell)
Vertex figure 64 {4,3,3,3,3}
(hexacross)
Coxeter group {\tilde{C}}_6, [4,3,3,3,3,4]
{\tilde{B}}_6, [4,3,3,3,31,1]
Dual self-dual
Properties vertex-transitive, edge-transitive, face-transitive, cell-transitive

The 6-cube honeycomb or hexeractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 6-space.

It is analogous to the square tiling of the plane and to the cubic honeycomb of 3-space.

There are many different Wythoff constructions of this honeycomb. The most symmetric form is regular, with Schläfli symbol {4,3,3,3,3,4}. Another form has two alternating 6-cube facets (like a checkerboard) with Schläfli symbol {4,3,3,3,31,1}. The lowest symmetry Wythoff construction has 64 types of facets around each vertex and a prismatic product Schläfli symbol {∞}6.

See also

References