On Symmetric Structures within Symmetric Solid Objects

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

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Section XXXX - A First Look at the 2 [ Quad-Type Structures ]

Summary for the Section :

• In this Section , we shall take a first look at the 2 [ Quad-Type Structures ] :
  • to bring-out the finer differences between the two .

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Flipping-Over the [ Red-Color Quad-Type Structure ] :

• Let us first bring-back the [ Red-Color Quad-Type Structure ] from the last Section :

  

  Let us now flip-over the entire [ Icosahedral Sphere ] to arrive at this :

  

  

  And we bring-in immediately the [ Magenta-Color Quad-Type Structure ] , as shown above , for a quick comparison .

• So , what is the difference here ?

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The Finer Difference :

• What we noticed here is that the 2 [ Quad-Type Structures ] do share a common [ piece ] , namely :
  • the [ curved triangular piece ] at-the-very-top of both the [ Magenta-Color Tetrahedron ] and the [ Red-Color Tetrahedron ] .

  Since the orientations of the 2 Tetrahedra are different , we can now come to the conclusion that :

  • the orientation of this [ piece ] with respect to the [ frame ] of the [ Magenta-Color Tetrahedron ]

    is different from :

  • the orientation of the same [ piece ] with respect to the [ frame ] of the [ Red-Color Tetrahedron ] .

• And we shall take a look at this finer difference , next .

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go to the next section : Section XXXXI - The Rotational Orientation of the [ Curved Triangular Pieces ]

go to the last section : Section XXXIX - Identifying 2 [ Quad-Type Structure ] for Our Analysis

return to the Symmetric Solid Objects HomePage

Original dated 2010-3-31