M. Rudin gave a triangulation of a tetrahedron with the property that after any small tetrahedron removed, the remaining part is not homeomorphic to a ball (An unshellable triangulation of a tetrahedron, Bull. Am. Math. Soc. (64), 1958, pp.~90--91). This example is not compatible with the tetrahedral rotation group $T_{12}$. Is there an unshellable triangulation invariant under the rotation group's action?