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We will examine the issue of diffeomorphism symmetry in simplicial models of(quantum) gravity, in particular for Regge calculus. We find that for asolution with curvature there do not exist exact gauge symmetries on thediscrete level. Furthermore we derive a canonical formulation that exactlymatches the dynamics and hence symmetries of the covariant picture. In thiscanonical formulation broken symmetries lead to the replacements of constraintsby so--called pseudo constraints. These considerations should be taken intoaccount in attempts to connect spin foam models, based on the Regge action,with canonical loop quantum gravity, which aims at implementing properconstraints. We will argue that the long standing problem of finding aconsistent constraint algebra for discretized gravity theories is equivalent tothe problem of finding an action with exact diffeomorphism symmetries. Finallywe will analyze different limits in which the pseudo constraints might turninto proper constraints. This could be helpful to infer alternativediscretization schemes in which the symmetries are not broken.

(Broken) Gauge Symmetries and Constraints in Regge Calculus