9 Variable Hexagon Projected from Hyper-Triangle


This is understood to be directly connected to the hexagonal face of a Cube Octahedral Cup geometry. It is also the dimensonally reduced version of the Cube Octahedron, though this is 2D or 3D and those Pascalloids are 3D or 4D

Combinatoric alg for the tripple summation of a triangle in to a hexagon:

Download XL file:
4 D 9-var Hexagon.xls

These spreadsheet calculations are also fully accurate and non-arbitrary. The Nine Variable Hexagonal Pascalloid now has an algabreic "explanation", however the geometric arrangement of terms is not yet implied by only that. It is in fact a five dimensional hyper-prism summed three times to generate the two-dimensional hexagonal output, as a combinatoric equation. Three sums can occur simultaneously, in a geometric way, not a divergent way, or perhaps a divergent sum that is spatially / geometrically balanced at a each stage.

There are actually nine variables used to form this dense hexagon, three overlapping. However now we have a "newly dicovered" algebraic equation for this pattern of 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
N = 12
N = 13
N = 14
N = 15
N = 16
N = 17