The $Z_k\times D_{k^{\mathrm{\prime }}}$ Brane Box Model

An example of a non-Abelian Brane Box Model, namely one corresponding to a $Z_k\times D_{k^{\mathrm{\prime }}}$ orbifold singularity of ${\text{C}}^3$, is constructed. Its self-consistency and hence equivalence to geometrical methods are subsequently shown. It is demonstrated how a group-theoretic twist of the non-Abelian group circumvents the problem of inconsistency that arise from na"{\i}ve attempts at the construction.