| 152 honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform tessellation |
| Family | 1k2 polytope |
| Schläfli symbol | {3,35,2} |
| Coxeter symbol | 152 |
| Coxeter-Dynkin diagram |   
|
| 8-face types | 142 151 
|
| 7-face types | 132 141 
|
| 6-face types | 122 {31,3,1}  {35} 
|
| 5-face types | 121 {34} 
|
| 4-face type | 111 {33} 
|
| Cells | {32}
|
| Faces | {3}
|
| Vertex figure | birectified 8-simplex: t2{37} 
|
| Coxeter group |  , [35,2,1]
|
Ingeometry, the 152 honeycomb is a uniform tessellation of 8-dimensional Euclidean space. It contains 142 and 151 facets, in a birectified 8-simplex vertex figure. It is the final figure in the 1k2 polytope family.
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 end of the 2-length branch leaves the 8-demicube, 151.
Removing the node on the end of the 5-length branch leaves the 142.
The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the birectified 8-simplex, 052.
| 1k2 figuresinn dimensions | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Space | Finite | Euclidean | Hyperbolic | ||||||||
| n | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |||
| Coxeter group |
E3=A2A1 | E4=A4 | E5=D5 | E6 | E7 | E8 | E9 = = E8+
|
E10 =  = E8++
| |||
| Coxeter diagram |
   
|
|
|
|
|
|
|
| |||
| Symmetry (order) |
[3−1,2,1] | [30,2,1] | [31,2,1] | [[32,2,1]] | [33,2,1] | [34,2,1] | [35,2,1] | [36,2,1] | |||
| Order | 12 | 120 | 1,920 | 103,680 | 2,903,040 | 696,729,600 | ∞ | ||||
| Graph | 
|
|
|
|
|
|
- | - | |||
| Name | 1−1,2 | 102 | 112 | 122 | 132 | 142 | 152 | 162 | |||
|
Fundamental convex regular and uniform honeycombs in dimensions 2–9
| ||||||
|---|---|---|---|---|---|---|
| Space | Family | 
|
|
|
|
 /  / 
|
| E2 | Uniform tiling | {3[3]} | δ3 | hδ3 | qδ3 | Hexagonal |
| E3 | Uniform convex honeycomb | {3[4]} | δ4 | hδ4 | qδ4 | |
| E4 | Uniform 4-honeycomb | {3[5]} | δ5 | hδ5 | qδ5 | 24-cell honeycomb |
| E5 | Uniform 5-honeycomb | {3[6]} | δ6 | hδ6 | qδ6 | |
| E6 | Uniform 6-honeycomb | {3[7]} | δ7 | hδ7 | qδ7 | 222 |
| E7 | Uniform 7-honeycomb | {3[8]} | δ8 | hδ8 | qδ8 | 133 • 331 |
| E8 | Uniform 8-honeycomb | {3[9]} | δ9 | hδ9 | qδ9 | 152 • 251 • 521 |
| E9 | Uniform 9-honeycomb | {3[10]} | δ10 | hδ10 | qδ10 | |
| E10 | Uniform 10-honeycomb | {3[11]} | δ11 | hδ11 | qδ11 | |
| En-1 | Uniform (n-1)-honeycomb | {3[n]} | δn | hδn | qδn | 1k2 • 2k1 • k21 |