Abstract
A conjecture is made that the weight space for 4D, mathcal{N} -extended supersymmetrical representations is embedded within the permutahedra associated with permutation groups \U0001d54ad. Adinkras and Coxeter Groups associated with minimal representations of 4D, mathcal{N} = 1 supersymmetry provide evidence supporting this conjecture. It is shown that the appearance of the mathematics of 4D, mathcal{N} = 1 minimal off-shell supersymmetry representations is equivalent to solving a four color problem on the truncated octahedron. This observation suggest an entirely new way to approach the off-shell SUSY auxiliary field problem based on IT algorithms probing the properties of \U0001d54ad.
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