On Symmetry Through-put linking 3-4-5-6-7 Dimension's ,
Octo-Symmetry for the { 4-Dimension Quasi-Octahedron } ,
and 2 Identical { 8-D Structures } oriented Symmetrically

by Frank C. Fung ( 1st published in July, 2017. )

Top Of Page

Section XIII - The Tri-Symmetry Analysis for { Set A / B / C }

Summary for the Section :

• In this Section , we shall do the Tri-Symmetry Analysis for { Set A / B / C } .

go to Top Of Page

Recalling { Set A / B / C } :

• Let us first recall { Set A } , { Set B } and { Set C } :

  

  

  

go to Top Of Page

Using { Set X } as the Temporary { 4 Axial-Directions } :

• Let us now bring back this set of relations for { Set X } :

  

  Applying the relation on-the-right above to { Set A / B / C } , we have :

  

  

  

  yielding :

  

  

  

go to Top Of Page

Using { Set Y } as the Temporary { 4 Axial-Directions } :

• Let us now bring back this set of relations for { Set Y } :

  

  Applying the relation on-the-right above to { Set A / B / C } , we have :

  

  

  

  yielding :

  

  

  

go to Top Of Page

Using { Set Z } as the Temporary { 4 Axial-Directions } :

• Let us now bring back this set of relations for { Set Z } :

  

  Applying the relation on-the-right above to { Set A / B / C } , we have :

  

  

  

  yielding :

  

  

  

go to Top Of Page

Summarizing :

• Let us now summarize our findings here :
  • via this table below :

    Temporary 4 Axial-Directions Set used for evaluating the Relative Positions	* * *	Relative Position for			* * *
    		the original Fixed- Position Set A	the original Fixed- Position Set B	the original Fixed- Position Set C
    *****************************	*	******	******	******	*
    4 Axial-Directions of { Set X }	*	Type C matrix	Type B matrix	Type A matrix	*
    4 Axial-Directions of { Set Y }	*	Type A matrix	Type C matrix	Type B matrix	*
    4 Axial-Directions of { Set Z }	*	Type A matrix	Type B matrix	Type C matrix	*

• Let us now make these statements :
  • Statement One :
    • When we switch from { Set Z } to { Set Y } as the { Temporary 4 Axial-Directions Set } or vice-versa :
      • the { Type A matrix } does not move while the other two (2) matrices exchange positions .

  • Statement Two :
    • When we switch from { Set Z } to { Set X } as the { Temporary 4 Axial-Directions Set } or vice-versa :
      • the { Type B matrix } does not move while the other two (2) matrices exchange positions .

  • Statement Three :
    • When switch from { Set X } to { Set Y } as the { Temporary 4 Axial-Directions Set } or vice-versa :
      • everybody moves in a { rotation-type order } .

go to Top Of Page

What's Next :

• We shall do the Tri-Symmetry Analysis for { Set D / E / F } , next .

go to Top Of Page

go to the next Section : Section XIV - The Tri-Symmetry Analysis for { Set D / E / F }

go to the last Section : Section XII - Set up for our Analysis on Tri-Symmetry

return to the Symmetry Through-put HomePage

Original dated 2017-7-23