  We generalise the concept of duality to lattice equations. We derive a novel
3 dimensional lattice equation, which is dual to the lattice AKP equation.
Reductions of this equation include Rutishauser's quotient-difference (QD)
algorithm, the higher analogue of the discrete time Toda (HADT) equation and
its corresponding quotient-quotient-difference (QQD) system, the discrete
hungry Lotka-Volterra system, discrete hungry QD, as well as the hungry forms
of HADT and QQD. We provide three conservation laws, we conjecture the equation
admits N-soliton solutions and that reductions have the Laurent property and
vanishing algebraic entropy.
