Quasi Quad-Symmetry

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

Section XII - Quasi Quad-Symmetry within the [ 24 Base Structural Patterns ]

In this Section , we shall take a look at [ Quasi Quad-Symmetry ] found within the [ 24 Base Structural Patterns ] .

And we shall attempt to split the [ 24 QSM-Patterns --- ALPHA Series ] into :
- 6 x [ sets of 4-elements Quasi Quad-Symmetric Patterns ] .

Let us now bring-in again the [ 24 Base Structural Patterns ] and also the [ 24 QSM-Patterns --- ALPHA Series ] ,
- for re-familiarization purposes :
And we simply note here that :
- [ Pattern A ] on the diagram of-the-right above is the same as the pattern [ Pattern AARON ] :
And we shall be using [ Patter AARON ] and [ Pattern A ] interchangeably in the remainder of this Section .

Let us now select one of the [ 4 Master Structural Patterns ] as the [ Anchor Pattern ] :
- and we shall select the [ Pattern on-the-left ] here , at-this-first-instance .

Let us now plug-in [ Pattern AARON ] / [ Pattern A ] as the [ Core Pattern ] for our Expansion-Mapping procedure :

And the [ Colors-to-Numbers Assignment Scheme ] here , based on the above , is then :

Color #1	Color #2	Color #3	Color #4	Color #5	Color #6	Color #7	Color #8
***********	***********	***********	***********	***********	***********	***********	***********
RED	CYAN	PURPLE	MAGENTA	GREEN	YELLOW	ORANGE	BLUE

We then have this as a result :

And the 4 patterns in the diagram on-the-right above are then :
- from-left-to-right , [ Pattern A ] , [ Pattern H ] , [ Pattern Z ] and [ Pattern Q ] respectively .

Let us now double-check , to make sure that the [ 4 Master Structural Patterns ] do yield [ Quasi Quad-Symmetric Patterns ] .

First , let us plug-in [ Pattern A ] as the [ Core Pattern ] to arrive at this :

Secondly , let us plug-in [ Pattern H ] as the [ Core Pattern ] to arrive at this :

Thirdly , let us plug-in [ Pattern Z ] as the [ Core Pattern ] to arrive at this :

Fourth-and-finally , let us plug-in [ Pattern Q ] as the [ Core Pattern ] to arrive at this :
And from these results , we can now conclude that :
- [ Pattern A ] , [ Pattern H ] , [ Pattern Z ] and [ Pattern Q ] do form a [ Quasi Quad-Symmetric Set ] .
- the [ 4 Master Structural Patterns ] we have above is indeed a [ set of quasi quad-symmetric Structural Patterns ] .

Let us now plug-in [ Patterns A / B / C / D / E / F ] as the [ Core Pattern ] ,
- to see what we might come up with .
Let us now plug-in [ Pattern A ] as the [ Core Pattern ] and do the Expansion-Mapping Procedure :

Let us now plug-in [ Pattern B ] as the [ Core Pattern ] and do the Expansion-Mapping Procedure :

Let us now plug-in [ Pattern C ] as the [ Core Pattern ] and do the Expansion-Mapping Procedure :

Let us now plug-in [ Pattern D ] as the [ Core Pattern ] and do the Expansion-Mapping Procedure :

Let us now plug-in [ Pattern E ] as the [ Core Pattern ] and do the Expansion-Mapping Procedure :

Let us now plug-in [ Pattern F ] as the [ Core Pattern ] and do the Expansion-Mapping Procedure :
And we see here that :
- we were able to separate the [ 24 QSM-Patterns ] into 6 sets of [ Quasi Quad-Symmetric Sets ] , with 4 elements in each set .