| quarter 7-cubic honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform 7-honeycomb |
| Family | Quarter hypercubic honeycomb |
| Schläfli symbol | q{4,3,3,3,3,3,4} |
| Coxeter diagram |       =  
|
| 6-face type | h{4,35},  h5{4,35},  {31,1,1}×{3,3} duoprism |
| Vertex figure | |
| Coxeter group |  ×2 = [[31,1,3,3,3,31,1]]
|
| Dual | |
| Properties | vertex-transitive |
Inseven-dimensional Euclidean geometry, the quarter 7-cubic honeycomb is a uniform space-filling tessellation (orhoneycomb). It has half the vertices of the 7-demicubic honeycomb, and a quarter of the vertices of a 7-cube honeycomb.[1] Its facets are 7-demicubes, pentellated 7-demicubes, and {31,1,1}×{3,3} duoprisms.
This honeycomb is one of 77 uniform honeycombs constructed by the 
| D7 honeycombs | |||
|---|---|---|---|
| Extended symmetry |
Extended diagram |
Order | Honeycombs |
| [31,1,3,3,3,31,1] | 
|
×1 |  , , , , , ,
|
| [[31,1,3,3,3,31,1]] |   
|
×2 | , , ,
|
| <[31,1,3,3,3,31,1]> ↔ [31,1,3,3,3,3,4] |
   ↔ 
|
×2 | ... |
| <<[31,1,3,3,3,31,1]>> ↔ [4,3,3,3,3,3,4] |
   ↔ 
|
×4 | ... |
| [<<[31,1,3,3,3,31,1]>>] ↔ [[4,3,3,3,3,3,4]] |
↔
|
×8 | ... |
Regular and uniform honeycombs in 7-space:
|
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 |