Polycubes have been a fruitful approach for all-hexahedral mesh generation, thanks to an attractive robustness/quality trade-off. Starting from a tetrahedral mesh of the input shape, a polycube can be easily represented by associating one of the six signed orthogonal direction ±{X, Y, Z} to boundary triangles, called labeling. Not all labelings induce polycubes, therefore validity criteria have been proposed. Despite satisfactory in most cases, they are neither necessary nor sufficient. By presenting failure cases, we open the discussion towards new approaches to discriminate between valid and invalid polycube labelings.