16 Variable Hexagon Projected from Hypercube


The origin of this algorythm is the ancient "Flower of Life" geometry, yet in my mathematical language, I reverse-engineer it from a hypercube into a slightly larger hexagon.

The only certain fact about this geometry is that a special algebra applies in this case.

I have not yet found a simple combinatoric solution, at least not one without many acceptions that works for all 'N' values, so there is no .xls file 'proof' for this one yet.

It is a fairly quantitative perfect Hexagon, meaning solid numbers over the whole Hexagon. As far as it may be useful, I finally found the way to produce these numbers as coefficients from that algebraic equation as follows.

If the terms were left with variables each equal to 1, the coefficients will multiply to create these exact numbers.





N = 0
N = 1
N = 2
N = 3
N = 4
N = 5
N = 6
N = 7
N = 8
N = 9
N = 10
N = 11

"...It looks beautifull, and even higher N values can be examined with the Pascal's Canvas 4.8 app."