On the 30-Rhombus Symmetric Solid Object

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

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Section XI - [ Axis of Penta-Symmetry ] within the [ 30-Rhombus S-S-O ]

Summary for the Section :

• In this Section , we shall identify the [ Axis of Penta-Symmetry ] within the [ 30-Rhombus S-S-O ] .

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Bringing-in the [ 30-Rhombus S-S-O ] from the last Section :

• Let us now bring-in the Third Version of the [ 30-Rhombus S-S-O ] from the last Section .

  

  And we have already established during our [ Second Attempt ] at the [ 30-Rhombus S-S-O ] that :

  • the line passing thru [ Point A ] and [ Point B ] as shown in the diagram in-the-middle above
    • is indeed an [ Axis of Penta-Symmetry ] .

  And we bring back this set of 3 diagrams from Section IX :

  

  • for the reader's quick review .

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How many [ Axis of Penta-Symmetry ] are there :

• The question then arises as to how many [ Axis of Penta-Symmetry ] are there ?

  And we bring back this set of 3 diagrams from the last Section :

  

  And we see here that [ Point A ] and [ Point B ] forming the [ Line-segment A-B ]

  • are Nodal-Points originally associated with the Icosahedron .

• Since the Icosahedron has exactly 12 Nodal-Points ,
  • it then follows that :
    • these 12 Nodal-Point can be divided to form exactly 6 pairs of [ opposite nodal-points ] .

  As such ,

  • there are exactly 6 [ Axis of Penta-Symmetry ] within the [ 30-Rhombus S-S-O ] .

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go to the next section : Section XII - [ Axis of Bi-symmetry ] within [ 30-Rhombus S-S-O ]

go to the last section : Section X - Third Attempt at the [ 30-Rhombus Symmetric Solid Object ]

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Original dated 2013-2-04