| Table 9
| n=10 |
9*.2 |
|
n=12 |
9*2.2.2 |
9*2.2:.2 |
9*2:.2:.2 |
| |
9*.2 0 |
|
|
9*2.2.2 0 |
9*2.2:.2 0 |
9*2:.2:.2
0 |
| |
|
|
|
9*2.2 0.2 |
9*2.2 0:.2 |
9*2:.2 0:.2
0 |
| n=11 |
9*2.2 |
9*2:2 |
|
9*2.2 0.2
0 |
9*2 0.2:.2 |
9*2 0:.2 0:.2
0 |
| |
9*2.2 0 |
9*2:2 0 |
|
9*2 0.2.2
0 |
9*2.2 0:.2
0 |
|
| |
9*2 0.2 |
9*2 0:2 0 |
|
9*2 0.2 0.2
0 |
9*2 0.2:.2
0 |
|
| |
9*2 0.2 0 |
|
|
|
9*2 0.2 0:.2 |
|
| |
|
|
|
|
9*2 0.2 0:.2
0 |
|
The KLs of the P(R)-subworld
derived from 9* are obtained by replacing bigons in the source
KLs by R-tangles not beginning with 1. Using the symmetry equivalents,
we reduce a complete derivation to a derivation from the corresponding
representatives. For n=10 we have the representative 9*2 (9*2
0) with P @
{(1)}; for n=11 two representatives: 9*2:2 (9*2 0:2
0) with P @
{(1,2)}, 9*2.2
(9*2:2 0, and all source links derived from 9*2.2)
with P @
{(1)(2)}. Their permutation
groups P have already been considered.
The next member (2×5)*
of the infinite class (2×k)*
is the basic polyhedron 10*- 5-antiprism, with the graph symmetry
group G=[2+,10] of order 20, generated by the rotational reflection
|
~
S
|
=(1,2,3,4,5,6,7,8,9,10) |
|
and by reflection
| R=(1)(2,5)(3,4)(6)(7,10)(8,9) |
|
According to
PET,
| ZG
= |
1
20 |
(t110+6t25+5t12t24+4t52+4t10), |
|
| ZG(x,1)=1+x+5x2+8x3+16x4+16x5+16x6+8x7+5x8+x9+x10, |
|
| ZG(x,x,1)=1+2x+15x2+56x3+194x4+428x5+ |
|
| 728x6+800x7+636x8+272x9+78x10 |
|
(10
£ n
£ 20).
For n=11 we have the representative 10*a ({1}) generating 2
source links 10*2, 10*2 0; for n=12 the representative
10*a.b ({1,2}, {1,3}, {1,6}, {1,7}, {1,9}) generating 3 source links 10*2.2, 10*2.2 0, 10*2 0.2 0. Taking
for n=11 the representative 10*2 (10*2 0) with P
@
{(1)}, we can obtain for n £
12 all links derived
from 10*.
  
|