An Approach to the 'I-CHING'

by Frank C. Fung - 1st published in December, 2004.

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1st Epilog : Thoughts on the Tetrahedra

( dated 2005-2-23 )

Topic I - The Tetrahedra :

Let us look, in general, at the Tetrahedra :

which has :

• 4 { nodal points } ,
• 6 Edges of equal-lengths ,
• 4 outer-surfaces, each an equilateral triangle.

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Topic II - The { ICG Cube } & the Tetrahedra :

Let us now bring back the { ICG Cube } :

• which is a { unit-cube } with 8 corners, or { nodal points } .

We note that we have now labeled the alternate { corners / nodal points } on the 'Cube' a different color ,

• namely 'Red-color' & 'Blue-color' respectively.

Let us now join the 4 { red-color nodal points } via the six (6) { red-color lines } , as shown below :

We have therefore constructed a Tetrahedra, as shown below :

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Topic III - The Tetrahedra in natural occurance :

The Tetrahedra is a shape that has many natural occurances.

For example, many { Crystalline Solids } exhibits either :

• the { Hexagonal Close-Pack} packing pattern ( hcp) , or

• the { Cubic Close-Pack } packing pattern ( ccp ) ;

  where each element has as many as 12 first-neighbors.

We have then marked, in 'red-color' , the { 4 nodal-points } of a Tetrahedra for the { Hexagonal Close-Pack } on the left-hand-side, as an example.

The Tetrahedra is therefore a shape central to the { Hexagonal Close-Pack } packing pattern.

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Topic IV - Going from '4' to '6' :

In { An Approach to the 'I-CHING' } , we went from :

• the [ { modulo 4 } / { parity-of-4 } ] in the { Ceremony with the 50 sticks }

onto :

• the { 6-lines } of the Hexagram .

But WHY , from '4' to '6' ?

May be the Tetrahedra will provide an early hint towards the answer .

• ( More thoughts later when we present the { ICG Game } . )

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original dated 2005-2-23