  It is conjectured that all decomposable (i.e. interior can be triangulated
without adding new vertices) polyhedra with vertices in convex position are
infinitesimally rigid and only recently has it been shown that this is indeed
true under an additional assumption of codecomposability (i.e. the interior of
the difference between the convex hull and the polyhedron itself can be
triangulated without adding new vertices).
  One major set of tools for studying infinitesimal rigidity happens to be
throughout the (negative) Hessian $M_T$ of the discrete Hilbert-Einstein
functional. Besides its theoretical importance, it provides the necessary
machinery to tackle the problem experimentally. To search for potential
counterexamples to the conjecture, one constructs an explicit family of
so-called $T$-polyhedra, all of which are weakly convex and decomposable, while
being non-codecomposable. Since infinitesimal rigidity is equivalent to a
non-degenerate $M_T$, one can let Mathematica search for the eigenvalues of
$M_T$ and gather experimental evidence that such a flexible, weakly convex and
decomposable $T$-polyhedron may not exist.
