On Symmetric Structures within Symmetric Solid Objects

by Frank C. Fung ( 1st published in March, 2010. )

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Section XXXIX - Identifying 2 [ Quad-Type Structures ] for Our Analysis

Summary for the Section :

• In this Section , we shall identify 2 particular [ Quad-Type Structures ] within the Icosahedron , namely :
  • the [ Magenta-Color Quad-Type Structure ] from the [ ALPHA Series ] , and
  • the [ Red-Color Quad-Type Structure ] from the [ OMEGA Series ] ;

  for our comparison and analysis on the finer difference between the 2 types of [ Quad-Type Structures ] ,

  • in the next 2 Sections .

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Bringing back the [ Isometric View ] :

• As we shall be using the [ Isometric View ] for viewing here in Part VIII ,
  • we now bring back this [ Isometric View ] for the Cube , for familiarization purposes .

  

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Identify the [ Magenta-Color Quad-Type Structure ] :

• Let us now bring-in the [ Icosahedral Sphere ] in the [ Isometric View ] ;
  • colored via the [ ALPHA Series - Quad-Type Structure Coloring Scheme ] .

    ( see Section XXV for details on the ALPHA / OMEGA Series Coloring Schemes ) .

  

• We can then identify the [ Magenta-Color Quad-Type Structure ] , via :
  • the [ centroidal-points ] of the [ 4 magenta-color pieces ] .

  

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Identify the [ Red-Color Quad-Type Structure ] :

• Let us now also bring-in the [ Icosahedral Sphere ] in the [ Isometric View ] ;
  • colored via the [ OMEGA Series - Quad-Type Structure Coloring Scheme ] .

  

• We can then identify the [ Red-Color Quad-Type Structure ] , via :
  • the [ centroidal-points ] of the [ 4 red-color pieces ] .

  

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Formation of the Cube :

• There is a particular reason as to why we have chosen this pair of [ Quad-Type Structures ] for our analysis :
  • the 4 [ magenta-color pieces ] and 4 [ red-color pieces ] are , in pairs , directly-opposite to one-another ,

  As such :

  • the 8 [ centroidal-points ] here are in fact the [ 8 corners of a Cube ] .

  

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go to the next section : Section XXXX - A First Look at the 2 [ Quad-Type Structures ]

go to the last section : Section XXXVIII - Duality Likage via the [ OHATS ( 120 Split ) Sphere ]

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Original dated 2010-3-31