On the 30-Rhombus Symmetric Solid Object

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

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Section VIII - First Attempt at the [ 30-Rhombus Symmetric Solid Object ]

Summary for the Section :

• In this Section , we shall make our first attempt to construct the [ 30-Rhombus Symmetric Solid Object ] .

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Bringing-in the Dodecahedron and the Icosahedron :

• Let us now bring-in the Standard Model of the Dodecahedron from Section IV :

  

  And we also bring-in the Standard Model of the Icosahedron from Section VI :

  

• We then combine the 20 Nodal-Points of the Dodecahedron and the 12 Nodal-Points of the Icosahedron :
  • to arrive at this 32 Nodal-Points Object as shown in the diagram in-the-middle below .

  

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The Resultant [ 30-Rhombus Symmetric Solid Object ] :

• We then present this First Version of the resultant [ 30-Rhombus Symmetric Solid Object ] :

  

  • Admitted , this First Version of the [ 30-Rhombus Symmetric Solid Object ] is extremely difficult to decipher at first sight .

• And the difficulties in viewing here arise mainly from two (2) sources :

  FIRST :

  • There are 30 Rhombuses here but :
    • only 12 Rhombuses showed up in the [ Front View ] ,

      and

    • another 12 Rhombuses showed up in the [ Transparent / See-Thru Back View ] .

    Six (6) Rhombus are in fact hidden-from-view :

  

  SECOND :

  • At this particular viewing angle , the 60 Edge-Lines showed up in only 3 directions :
    • as marked-off in [ magenta-color ] , [ light-green color ] and [ cyan-color ]
      • in this set of 3 diagrams below .

  

  This makes it extremely difficult to read :

  • the [ ridge-effect ] for [ 2 same-color lines coming into a shared Nodal-Point ] .

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Identify a particular set of 6 Rhombuses :

• However , our First Attempt here does serve a specific purpose .

  Let us now identify this particular set of 6 rhombuses ,

  • as marked-off in [ cyan-color ] below .

  

  

  • And we see here that :
    • the 1st pair of rhombuses are located at the tips of the [ +X / -X ] Axis ,

    • the 2nd pair of rhombuses are located at the tips of the [ +Y / -Y ] Axis ,

    • the 3rd pair of rhombuses are located at the tips of the [ +Z / -Z ] Axis .

• And the 6 rhombuses here , when taken together as a whole ,
  • do form a Hexa-Symmetric Structure .

  

  

  We shall be coming back to the above set of 6 diagrams later ,

  • when we take a closer look at [ Hexa-Symmetric Structures ] within the [ 30-Rhombus S-S-O ] in Section XIII .

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go to the next section : Section IX - Second Attempt at the [ 30-Rhombus Symmetric Solid Object ]

go to the last section : Section VII - A Quick Review of the Rhombus

return to the 30-Rhombus Symmetric Solid Object HomePage

Original dated 2013-2-04