# On Dehn's infinitesimal rigidity theorem

Dehn's theorem states that any simplicial strictly convex polyedron P in Euclidean 3-space is infinitesimally rigid (that is, any non-trivial first order deformation of P induces a variation of its edges lengths). But many authors write « convex polyhedra are infinitesimally rigid »... Are the conditions « simplicial » and « strictly » necessary ?

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It is easy to see what is meant by a non-strictly convex polyhedron: some edges have dihedral angle of $\pi.$ –  Igor Rivin Feb 26 '12 at 20:23