| 222 honeycomb | |
|---|---|
| (no image) | |
| Type | Uniform tessellation |
| Coxeter symbol | 222 |
| Schläfli symbol | {3,3,32,2} |
| Coxeter diagram |      
|
| 6-face type | 221 
|
| 5-face types | 211 {34} 
|
| 4-face type | {33}
|
| Cell type | {3,3}
|
| Face type | {3}
|
| Face figure | {3}×{3} duoprism |
| Edge figure | {32,2} 
|
| Vertex figure | 122 
|
| Coxeter group | , [[3,3,32,2]] |
| Properties | vertex-transitive, facet-transitive |
In geometry, the 222 honeycomb is a uniform tessellation of the six-dimensional Euclidean space. It can be represented by the Schläfli symbol {3,3,32,2}. It is constructed from 221 facets and has a 122 vertex figure, with 54 221 polytopes around every vertex.
Its vertex arrangement is the E6 lattice, and the root system of the E6 Lie group so it can also be called the E6 honeycomb.