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We prove that local operations that preserve all symmetries, as e.g. dual,truncation, ambo, or join,, as well as local operations that preserve allsymmetries except orientation reversing ones, as e.g. gyro or snub, preservethe polyhedrality of simple embedded graphs. This generalizes a result by Moharproving this for the operation dual. We give the proof based on an abstractcharacterization of these operations, prove that the operations are welldefined, and also demonstrate the close connection between these operations andDelaney-Dress symbols. We also discuss more general operations not coming from3-connected simple tilings of the plane.

On Local Operations that Preserve Symmetries and on Preserving Polyhedrality of Embeddings