  Adinkras are combinatorial objects developed to study 1-dimensional
supersymmetry representations. Recently, 2-d Adinkras have been developed to
study 2-dimensional supersymmetry. In this paper, we classify all 2-d Adinkras,
confirming a conjecture of T. H\"ubsch. Along the way, we obtain other
structural results, including a simple characterization of H\"ubsch's
even-split doubly even code.
