210 Physical Symmetric Sets

On 8-Colors Combinatorics and [ Quasi 24-Symmetry ]

Section XXXIV - Setting up the 210 [ sets-of-24 ] with Physical Symmetries

In this Section , we shall list-out the procedure for dividing the [ Reduced Set of 5,040 Configurations ]
- into 210 sets of [ 24 QSM-Configurations ] .
And the [ Structural Mapping relations ] here within each [ set-of-24 ] are primarily physical in nature .

Let bring-back , at this point , [ Configuration Annapurna ] and [ Configuration Mount Robson ] :
- for our use in this Section .
Let us recall that :
- If we started-out with [ Configuration Annapurna ] , and :
  - permitted only [ 2-notch ( 180 degrees ) Half-on-Half rotations ] in the [ -X / -Y / -Z Axial-Directions ] ;
  then we can only reach a [ Reduced Set of 5,040 configurations ] ,
  - as per our discussions in Section XVIII of this paper .
Let us now proceed to split the [ Reduced Set of 5,040 configurations ] into the 210 sets of [ 24 QSM-Configurations ] .

Step One :
- We bring-in [ Configuration Annapurna ] and apply it to [ Position A ] in the Linkage Diagram on-the-right below :
Step Two :
- We bring-in [ Configuration Mount Robson ] and apply it to [ Position A ] in the Linkage Diagram on-the-right below :
Step Three :
- We randomly pick any one of the remaining configurations and apply it to [ Position A ] in the Linkage Diagram ;
  - to knock-off another set of [ 24 QSM-Configurations ] .
Step Four :
- We repeat [ Step Three ] above until all of the [ 5,040 configurations ] have been knocked-off .
And we would now have the 210 [ sets-of-24 ] .

Let us point-out here that :
- In the Splitting Procedure above ,
  - The [ Fu-Hei Scheme of Fixed-Posistions ] was not involved and
    we did not make use of any [ Read-Off Order ] for the fixed-positions ;
  - [ Colors-to-Numbers Conversion Schemes ] are also not involved .
As such , the symmetric properties for the [ sets-of-24 ] are primarily physical in nature ,
- arising-from and governed-by the physical phenomenon of the [ 2-notch rotations ] .

And we shall be looking at , next :
- what happens when we do the conversion to the [ 8-colors sequences ] using different [ Read-Off Orders ] .