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It is conjectured that all decomposable (i.e. interior can be triangulatedwithout adding new vertices) polyhedra with vertices in convex position areinfinitesimally rigid and only recently has it been shown that this is indeedtrue under an additional assumption of codecomposability (i.e. the interior ofthe difference between the convex hull and the polyhedron itself can betriangulated without adding new vertices).  One major set of tools for studying infinitesimal rigidity happens to bethroughout the (negative) Hessian $M_T$ of the discrete Hilbert-Einsteinfunctional. Besides its theoretical importance, it provides the necessarymachinery to tackle the problem experimentally. To search for potentialcounterexamples to the conjecture, one constructs an explicit family ofso-called $T$-polyhedra, all of which are weakly convex and decomposable, whilebeing non-codecomposable. Since infinitesimal rigidity is equivalent to anon-degenerate $M_T$, one can let Mathematica search for the eigenvalues of$M_T$ and gather experimental evidence that such a flexible, weakly convex anddecomposable $T$-polyhedron may not exist.

Are all Weakly Convex and Decomposable Polyhedral Surfaces Infinitesimally Rigid?