On the 30-Rhombus Symmetric Solid Object

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

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Section III - A Quick Review of the Pentagon

Summary for the Section :

• In this Section , we shall do a quick review of the Pentagon ,
  • in preparation of our structural dimensioning of the Dodecahedron in the next Section .

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Bringing-in the Pentagon :

• Let us first bring-in this Pentagon , as shown on-the-left below , and :
  • mark-off the distance from the [ Centroidal-Point of the Pentagon ] to [ any one of the five (5) Nodal-Points ]
    • as the distance [ R ] , as shown .

  

• Let us define , at this point :
  • the distance [ L-sub-S ] as the length of the [ Side of the Pentagon ] , i.e. :
    • 

  and

  • the distance [ L-sub-D ] as the length of the [ Cross-Diagonal of the Pentagon ] , i.e. :
    • 

    as shown in the diagrams in-the-middle and on-the-right above .

  Consequently , we have :

  • for the distance [ L-sub-S ] :
    

    yielding :

    • 

  • for the distance [ L-sub-D ] :
    • 

      or alternately :

    • 

      yielding :

    • 

• Adn with this information in-hand ,
  • we are now ready to do the structural dimensioning of the Dodecahedron , next .

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go to the next section : Section IV - Structural Dimensioning of the Dodecahedron

go to the last section : Section II - Outline on the Method of Construction

return to the 30-Rhombus Symmetric Solid Object HomePage

Original dated 2013-2-04