Enumeration
edit| Coxeter group | Extended symmetry |
Honeycombs (with Branko Grünbaum's indices) |
Chiral extended symmetry |
Alternation honeycombs | ||
|---|---|---|---|---|---|---|
[4,3,4]   |
[4,3,4]    |
6 |  22 | 7 | 8 9 | 25 | 20
|
[1+,4,3+,4,1+] | (2) |  1 | -
|
| [2+[4,3,4]] = |
(1) | 22
|
[2+[(4,3+,4,2+)]] | (1) | 1
| |
| [2+[4,3,4]] |
1 | 28
|
[2+[(4,3+,4,2+)]] | (1) | -
| |
| [2+[4,3,4]] |
2 | 27
|
[2+[4,3,4]]+ | (1) | -
| |
[4,31,1]   |
[4,31,1]  |
4 |  1 | 7 | 10 | 28
|
|||
[1[4,31,1]]=[4,3,4]  = |
(7) | 22 | 7 | 22 |  7 | 9 | 28 | 25
|
[1[1+,4,31,1]]+ | (2) | 1 |  -
| |
| [1[4,31,1]]+ =[4,3,4]+ |
(1) | -
| ||||
[3[4]]  |
[3[4]] | (none) | ||||
| [2+[3[4]]]
|
1 |  6
|
||||
| [1[3[4]]]=[4,31,1]
|
(2) |  1 | 10
|
||||
| [2[3[4]]]=[4,3,4]
|
(1) | 7
|
||||
| [(2+,4)[3[4]]]=[2+[4,3,4]]
|
(1) | 28
|
[(2+,4)[3[4]]]+ = [2+[4,3,4]]+ |
(1) |  -
| |
