On the 30-Rhombus Symmetric Solid Object

by Frank C. Fung ( 1st published in February, 2013. )

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Section XVI - Co-Planar Axis within the [ 30-Rhombus S-S-O ]

Summary for the Section :

• In this Section , we shall take a quick look at co-planar axis within the [ 30-Rhombus S-S-O ] .

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Bringing-in the [ 30-Rhombus S-S-O ] :

• Let us now bring-in this version of the [ 30-Rhombus S-S-O ] :

  

  and recall that :

  • we were able to split it into five (5) [ Hexa-Symmetric Structures ] .

  

• Let us now select any one of the 15 axis above for our analysis to follow ,
  • and we simply select this particular axis as shown below for our further investigation .

  

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Set of [ 3 Orthogonal Axis ] :

• We simply take note here that :
  • the [ selected axis ] is a member of a set of [ 3 orthogonal axis ] as shown below .

  

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2 Sets of [ 5 Co-Planar Axis ] :

• We simply take note here that :
  • the [ selected axis ] is a member of this first set of [ 5 co-planar axis ] as shown below .

  

  • the [ selected axis ] is also a member of this second set of [ 5 co-planar axis ] as shown below .

  

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2 Sets of [ 3 Co-Planar Axis ] :

• We simply take note here that :
  • the [ selected axis ] is a member of this first set of [ 3 co-planar axis ] as shown below .

  

  • the [ selected axis ] is also a member of this second set of [ 3 co-planar axis ] as shown below .

  

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Summarizing :

• Let us simply state here that :
  • for each-and-every one of the 15 axis here :
    • it is a member of a set of [ 3 orthogonal axis ] ,

    • it is a member of a first set of [ 5 Co-planar axis ] ,

    • it is a member of a second set of [ 5 Co-planar axis ] ,

    • it is a member of a first set of [ 3 Co-planar axis ] , and

    • it is a member of a second set of [ 3 Co-planar axis ] .

  

• Isn't that interesting !

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go to the next section : Section XVII - Reason for calculating the [ Tangent of 9-degrees ]

go to the last section : Section XV - [ Axis of Tri-Symmetry ] within the [ 30-Rhombus Symmetric Solid Object ]

return to the 30-Rhombus Symmetric Solid Object HomePage

Original dated 2013-2-04