| bgcolor=#e7dcc3 colspan=2 | 251 honeycomb | |
|---|---|---|
| bgcolor=#ffffff align=center colspan=2 | (No image) | |
| Type | Uniform tessellation | |
| Family | 2k1 polytope | |
| Schläfli symbol | ||
| Coxeter symbol | 251 | |
| Coxeter-Dynkin diagram | ||
| 8-face types | 241 | |
| 7-face types | 231 | |
| 6-face types | 221 | |
| 5-face types | 211 | |
| 4-face type | ||
| Cells | ||
| Faces | ||
| Edge figure | 051 | |
| Vertex figure | 151 | |
| Edge figure | 051 | |
| Coxeter group | {\tilde{E}}8 |
It is created by a Wythoff construction upon a set of 9 hyperplane mirrors in 8-dimensional space.
The facet information can be extracted from its Coxeter-Dynkin diagram.
Removing the node on the short branch leaves the 8-simplex.
Removing the node on the end of the 5-length branch leaves the 241.
The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the 8-demicube, 151.
The edge figure is the vertex figure of the vertex figure. This makes the rectified 7-simplex, 051.