  A conjecture is made that the weight space for 4D, $\cal N$-extended
supersymmetrical representations is embedded within the permutahedra associated
with permutation groups ${\mathbb{S}}{}_{d}$. Adinkras and Coxeter Groups
associated with minimal representations of 4D, $\cal N$ = 1 supersymmetry
provide evidence supporting this conjecture. It is shown the appearance of the
mathematics of 4D, $\cal N$ = 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
${\mathbb{S}}{}_{d}$.

High Energy Physics - Theory