posted on Feb, 27 2014 @ 02:39 PM
reply to post by mbkennel
You seem to have a good grasp on the topic at hand. I was wondering if you'd like to collaborate or just possibly run through an algorithm I've
been brainstorming for a little while now.
It goes as follows...
Using the geometry of the Cuboctahedron as a basis for computation with regards to vertices acting as the elements that make up a given set when
partitioning the Cartesian coordinates of said polyhedron. This is to be done using a base-12 or dozenal number system.
Being that the vertices of the Cuboctahedron are identical, this can then parallel binary golay code that provides a check sum system of computation.
Golay already uses a message length of 12 as well as a 24 block length with a distance of 8. Being that the cuboctahedron is made of 12 vertices that
are in a way error-correcting code when the geometry is computationally satisfied. The cuboctahedron additionally has 24 identical edges that
parallel Golay's 24 block length, and is achievable using 8 bits or 8 bit architecture already being used today that correlates with the Golay
distance of 8.
when decomposed, the cuboctahedrong becomes a octahedron + 8 irregular but equal octahedras of convex hull architecture while removing two opposite
vertices. This then paralleling cell-first projection of a 24-cell into 3rd dimension and under this projection the forming a projection envelope
that can be decomposed into 6 squares + 1 octahedron + 8 irregular octahedra.
These elements correspond with the images of the six octahedral cells in the 24-cell with regards to the nearest and furthest cells from the 4d view
point along with the 8 pairs of cells respectively.
Thus solving the allusive algorithmic problem of finding the convext hull of a finite set of poins in the plane or low-dimension euclidean speaces by
reverse engineering or re-composing the set back into cuboctahedron form in accordance with a cantellated 16-cell construction. Through 12
permutations in 4-space now alternatively using cartesian coordinates of edge length of ^(1/2) centered at the origin of .....
then sphere packing -- hupercube--- 24 dimensional leech lattice using duodecimal and given a binary translation.
if that makes sense? I'm sure it doesn't... but what I'm getting at is all there....
result... infinite error-correcting processing utilizing the fractal nature of the cuboctahedron with infinite partitions from which even 1 point can
be taken from each to create a new set that now CAN be measured using cartesian coordinates all encompassed by satisfying a geometry. 16,63,65