| quarter 5-cubic honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform 5-honeycomb |
| Family | Quarter hypercubic honeycomb |
| Schläfli symbol | q{4,3,3,3,4} |
| Coxeter-Dynkin diagram |       =  
|
| 5-face type | h{4,33},  h4{4,33}, 
|
| Vertex figure |  Rectified 5-cell antiprism or Stretched birectified 5-simplex |
| Coxeter group |  ×2 = [[31,1,3,31,1]]
|
| Dual | |
| Properties | vertex-transitive |
Infive-dimensional Euclidean geometry, the quarter 5-cubic honeycomb is a uniform space-filling tessellation (orhoneycomb). It has half the vertices of the 5-demicubic honeycomb, and a quarter of the vertices of a 5-cube honeycomb.[1] Its facets are 5-demicubes and runcinated 5-demicubes.
This honeycomb is one of 20 uniform honeycombs constructed by the
| D5 honeycombs | |||
|---|---|---|---|
| Extended symmetry |
Extended diagram |
Extended group |
Honeycombs |
| [31,1,3,31,1] | 
|
|
|
| <[31,1,3,31,1]> ↔ [31,1,3,3,4] |
    ↔ 
|
×21 = 
|
 , , ,
|
| [[31,1,3,31,1]] |
|
×22
|
,
|
| <2[31,1,3,31,1]> ↔ [4,3,3,3,4] |
   ↔ 
|
×41 = 
|
, , , , ,
|
| [<2[31,1,3,31,1]>] ↔ [[4,3,3,3,4]] |
↔
|
×8 = ×2
|
, ,
|
Regular and uniform honeycombs in 5-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 |