On the 30-Rhombus Symmetric Solid Object

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

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Section II - Outline on the Method of Construction

Summary for the Section :

• In this Section , we shall outline the method of construction for the [ 30-Rhombus Symmetric Solid Object ] .

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Identifying the Key Construction Criteria :

• First-of-all , we take note here that :
  • the Dodecahedron has exactly 30 edges , and :
    • the mid-points of the [ 30 Edges ] are equi-distant from the Center of the Dodecahedron ;

  • the Icosahedron also has exactly 30 edges , and :
    • the mid-points of the [ 30 Edges ] are equi-distant from the Center of the Icosahedron .

  And based on the above , our proposal here is then :

  • IF :
    • we were able to resize the Dodecahedron and the Icosahedron in a special manner ,

      so that :

      • the [ distance from the mid-point of an Edge to the Center ] is the same for both the Dodecahedron and the Icosahedron ,

    THEN :

    • there exists a possibility that we can orient the Dodecahedron and the Icosahedron in a special manner ,

      so that :

      • the [ edges of the Dodecahedron ] and the [ edges of the Icosahedron ] intersect at right-angles .

  And the two (2) edges , one from the Dodecahedron and one from the Icosahedron ,

  • would then become the major-axis and the minor-axis of the rhombus .

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Outline of the Construction Procedure :

• Our Construction procedure for the [ 30-Rhombus Symmetric Solid Object ] is as follows :
  • First ,
    • We construct our Standard Model for the Dodecahedron , so that :
      • the mid-points of the 30 edges are at the distance [ 1.0 ] away from the center .

  • Next ,
    • We construct our Standard Model for the Icosahedron , so that :
      • the mid-points of the 30 edges are at the distance [ 1.0 ] away from the center .

  • We can then combine the above-said Dodecahderon and Icosahedron ,
    • ensuring that :
      • the 30 edges from the Dodecaherdon and the 30 edges from the Icosahedron

        do intersect at their mid-points and at right-angles .

  The 32 Nodal-Points of the [ 30-Rhombus Symmetric Solid Object ] will then be made-up-of :

  • the 20 Nodal-Points from the Dodecahedron and the 12 Nodal-Points from the Icosahedron .

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go to the next section : Section III - A Quick Review of the Pentagon

go to the last section : Section I - Introduction

return to the 30-Rhombus Symmetric Solid Object HomePage

Original dated 2013-2-04