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Integrable discrete differential geometry of ‘plated’ membranes in equilibrium

Recently, it has been established that a well-known system of classical shell theory descriptive of membranes in equilibrium is, in fact, amenable to the techniques of soliton theory. Here, it is demonstrated that its canonical discrete counterpart governing ‘plated’ membranes in equilibrium is likewise integrable in that it admits both a parameter-dependent linear representation (Lax pair) and a Bäcklund transformation.