A Discrete Parametrized Surface Theory in ℝ3

We propose a discrete surface theory in $\mathbb R^3$ that unites the most prevalent versions of discrete special parametrizations. This theory encapsulates a large class of discrete surfaces given by a Lax representation and, in particular, the one-parameter associated families of constant curvature surfaces. The theory is not restricted to integrable geometries, but extends to a general surface theory.