The Octahedral geometry is coincidentally that of the Carbon atom, and the crystalline form of the Fouride crystal.

Given we start with the seed number [1] and proceed a 3D SUM[] algorhythm to the 5x5 space I have programmed in Flah 8, I am able to take several screen shots for each iteration of N.

The first iteration is of course the pure suggestion of [1] unit at each corner of the Octahedron. Whether this [1] at each direction of the Octahedron represents a Corner, a Verticie, or a Vector, it is all the same to me. There may be a deep underlying pattern, and ways to decoratively derive the golden mean. It is all the same to me. There is a formula to cover it's algebra f(N), recently discovered. However the Combinatoric formula I have found is also geometrically sound.

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And the great Octahedral algebra expansion takes the form:



Three angles expressing: sum total = 62 = 36, Octahedral
Three angles expressing: sum total = 63 = 216, Octahedral
Three angles expressing: sum total = 64 = 1,296 ; Octahedral
Three angles expressing: sum total = 65 = 7,776 ; Octahedral
Three angles expressing: sum total = 66 = 46,656 ; Octahedral
Three angles expressing: sum total = 67 = 279,936 ; Octahedral, central focus
Three angles expressing: sum total = 68 = 1,679,616 ; Octahedral, central focus