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. )

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Section I - Introduction

Introduction :

• This paper started out as an attempt to achieve a better understanding of
  • the { 28 Symmetric Lines in 7-Dimension } .

  But we branched off onto other topics , in this sequence :

  • in Part II ,
    • we used an extension of the { 28 Symmetric Lines in 7-D } procedure to come up with :
      • 35 Symmetric Lines orthogonal to the { Line-Of-Concern } .

      It happens that :

      • the 35 Lines and the { Line-Of-Concern } itself are lines found within :
        • the { 128 Cross-Diagonal Lines of the 8-D Quasi-Cube } framework .

  • in Part III ,
    • we concentrated on Symmetry in 4-D and the 96-triangles { Quasi-Octahedron } .

  • in Part IV ,
    • we split the { 8-D Quasi-Cube } into 2 identical { 64-Lines Structures } ,
      • and looked at their relative orientations .

  • in Part V ,
    • we split the { 6-D Quasi-Cube } into 2 identical { 16-Lines Structures } ,
      • with the 16 Lines within each Structure intersecting one-another at the angle of [ 70.53 degrees ] .

      and followed closely on the mechanics as to how the { 16 Symmetric Lines in 6-D } degenerates into :

      • { 10 Symmetric Lines in 5-D } ,
      • { 6 Symmetric Lines in 4-D } ,
      • { 4 Symmetric Lines in 3-D } .

• A lot of work ahead , no doubt .

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go to the next Section : Section II - Defining the { 8-Dimension Quasi-Cube }

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Original dated 2017-7-23