On Symmetric Structures within Symmetric Solid Objects

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

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Section XXXIII - Duality : Tetrahedron vs. Tetrahedron

Summary for the Section :

• In this Section , we shall take a look at the Duality of :
  • Tetrahedron vs. Tetrahedron .

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The Process of Duality :

• Let us now bring-in again the [ Tetrahedral Sphere ] :

  

  Let us now identify the [ centroidal points ] for each of the 4 [ curved triangular faces ] :

  • as marked-off via the 4 [ blue-color dots ] in the set of diagrams below .

  

• We note here that the 4 [ blue-color dots ] are in fact the 4 [ nodal-points ] for another [ Tetrahedral Sphere ] :

  

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The Duality :

• Very simply , the two (2) different [ Tetrahedral Spheres ] are related :
  • via the [ centroidal points ] of their [ curved triangular faces ] .

  In other words :

  • The [ centroidal points ] of the [ 1st Tetrahedral Sphere ] are the [ nodal points ] for the [ 2nd Tetrahderal Sphere ] , and :
  • The [ centroidal points ] of the [ 2nd Tetrahedral Sphere ] are the [ nodal points ] for the [ 1st Tetrahderal Sphere ] .

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go to the next section : Section XXXIV - Duality Linkage via the [ TFS ( 24-Split ) Sphere ]

go to the last section : Section XXXII - Ratio-Of-Areas and the Egyptian Fractions

return to the Symmetric Solid Objects HomePage

Original dated 2010-3-31