For s = 4 and l
£ 12,
the polyhedral generating braids and their corresponding KLs are given
in the following table, with the notation for basic polyhedra with 12 crossings
according to A. Caudron (1982):
| l = 10 |
|
AbAbACbdCd |
|
.2 2 1 |
|
l = 12 |
|
AbAbACbdCdCd |
|
12J |
| l = 10 |
|
AbACbCbdCd |
|
.2 1.2 1 |
|
l = 12 |
|
AbAbACdCbCdC |
|
11***:.2 0 |
| l = 10 |
|
AbACbdCbdC |
|
.2 1:2 1 0 |
|
l = 12 |
|
AbAbCbAbdCbd |
|
9*2 2 |
| l = 10 |
|
AbACdCbCdC |
|
.2 2:2 |
|
l = 12 |
|
AbAbCbCdCbCd |
|
8*2 1 1::2
0 |
|
|
|
|
|
|
l = 12 |
|
AbAbCbdCbCdC |
|
8*2 1 1 0:.2
0 |
| l = 11 |
|
AbAbACbCdCd |
|
.2 1 1 1 1 |
|
l = 12 |
|
AbAbCbdCbdCd |
|
9*2 1 1 |
| l = 11 |
|
AbAbCbCbdCd |
|
.2 1 1.2 1 0 |
|
l = 12 |
|
AbAbCdCbCdCd |
|
8*2 1 1 1
0 |
| l = 11 |
|
AbAbCbdCbdC |
|
.2 1 1:2 1 |
|
l = 12 |
|
AbACbAdCbdCd |
|
12L |
| l = 11 |
|
AbAbCdCbCdC |
|
.2 1 1 1:2 |
|
l = 12 |
|
AbACbCbCbdCd |
|
8*2 1 0.2
1 0 |
| l = 11 |
|
AbACbACbdCd |
|
9*2 1 0 |
|
l = 12 |
|
AbACbCbdCbCd |
|
9*.2 1:.2 |
| l = 11 |
|
AbACbCdCbCd |
|
8*2 1 0::2
0 |
|
l = 12 |
|
AbACbCbdCbdC |
|
8*2 1 0:.2
1 0 |
| l = 11 |
|
AbACbCdCdCd |
|
.2 2 1 1 |
|
l = 12 |
|
AbACbCdCbCdC |
|
9*2 1:2 |
| l = 11 |
|
AbACbdCbCdC |
|
8*2 1:.2 0 |
|
l = 12 |
|
AbACbCdCbdCd |
|
10**:2 1 0 |
| l = 11 |
|
AbACdCbCdCd |
|
8*2 2 0 |
|
l = 12 |
|
AbACbdCbCdCd |
|
10**.2 1 |
|
|
|
|
|
|
l = 12 |
|
AbACbdCbdCdC |
|
10**:2 1 |
| l = 12 |
|
AbAbAbACbdCd |
|
8*2 2 1 0 |
|
l = 12 |
|
AbCbAbCdCbCd |
|
10**:2 0::.2
0 |
| l = 12 |
|
AbAbACbAbdCd |
|
9*.2 2 |
|
l = 12 |
|
AbCbACbdCbCd |
|
10**2 0::.2
0 |
|
For W = (Ab)n
(n ³
2), w1
= ACbdCdCd the family of basic polyhedra beginning with 12J (AbAbACbdCdCd)
is obtained, and for W = (Ab)n (n
³ 1),
w1 = ACbAdCbdCd the family of basic polyhedra beginning with
12L (AbACbAdCbdCd) is obtained.
  
|