A Different Kind of Hexa-Symmetry

On the 30-Rhombus Symmetric Solid Object

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

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Section XXII - Investigating a different kind of Hexa-Symmetry

Summary for the Section :

In this Section , we shall take a quick look at a different kind of Hexa-Symmetry .

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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 the [ 30-Rhombus S-S-O ] into five (5) [ Hexa-Symmetric Structures ] :

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Selecting a [ Hexa-Symmetric Structure ] as the starting-point :

Let us now select any one of the 5 [ Hexa-Symmetric Structures ] above as the starting-point of our investigations in this Section ,
- and we shall now select the [ light-green color ] Hexa-Symmetric Structure here ,
  - solely because the orientation here does give us a slightly better viewing angle .

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Constructing a new-and-different [ Hexa-Symmetric Structure ] :

Let us now take the 6-rhombus [ Hexa-Symmetric Structure ] above and do some re-coloring .

We shall now :
- color the 1st pair of [ opposite rhombuses ] red-color ,
- color the 2nd pair of [ opposite rhombuses ] dark-green-color , and
- color the 3rd pair of [ opposite rhombuses ] blue-color .
Let us now also color :
- each set of 4 pieces adjacent to the [ red-color rhombuses ] the color [ magenta ] ,
- each set of 4 pieces adjacent to the [ dark-green-color rhombuses ] the color [ light-green ] , and
- each set of 4 pieces adjacent to the [ blue-color rhombuses ] the color [ cyan ] .
Now , we ask this question :
- Are the following 6 Structures identical in shape :
  - the 2 [ 5-rhombus combination in red / magenta colors ] ,
  - the 2 [ 5-rhombus combination in dark-green / light-green colors ] , and
  - the 2 [ 5-rhombus combination in blue / cyan colors ] .
Indeed they are :
- And now we have a new-and-different Hexa-Symmetric Structure ,
  - but this is not a Cube !

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Something for the Adventurous :

Let us now bring-in this set of diagrams from Section IV and Section VI
- for the adventurous , author and reader alike .
No further comments is warranted here :
- otherwise we might put the creativity of the adventurous in jeopardy .

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go to the next section : Section XXIII - Concluding Remarks

go to the last section : Section XXI - Constructing the [ 12-Rhombus Symmetric Solid Object ]

return to the 30-Rhombus Symmetric Solid Object HomePage

Original dated 2013-2-04