Discrete light-cone quantization on a twisted torus

Recently it has been demonstrated by Dienes and Mafi that the physics of toroidal compactified models of extra dimensions can depend on the shape angle of the torus. Toroidal compactification has also recently been used as a regulator for numerical solutions of supersymmetric field theories in 2+1 dimensions. The question is: does the shape angle of the torus also affect the physics in this situation? Clearly a numerical solution should be independent of the shape of the space on which we compactify, at least when the regulator is removed. We show that, for standard discrete light-cone quantization with transverse parity invariance, toroidal compactification is only allowed for a specific set of shape angles and for that set of shape angles the numerical solutions are unchanged.