  The main result of this paper is a discrete Lawson correspondence between
discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. This is a
correspondence between two discrete isothermic surfaces. We show that this
correspondence is an isometry in the following sense: it preserves the metric
coefficients introduced previously by Bobenko and Suris for isothermic nets.
Exactly as in the smooth case, this is a correspondence between nets with the
same Lax matrices, and the immersion formulas also coincide with the smooth
case.
