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We derive fundamentally new equations that are satisfied by first-orderflexes of a flexible polyhedron. Moreover, we indicate two sources of such newequations. These sources are the Dehn invariants and rigidity matrix. Theequations derived provide us with fundamentally new necessary conditions forthe extendibility of a first-order flex of a polyhedron to its flex.

Necessary conditions for the extendibility of a first-order flex of a polyhedron to its flex