Biswas–Pal–Tomar's rigidity conjecture for the hexablock

Let $\mathbb{H}$ denote the hexablock, let $G(\mathbb{H})$ be the group of explicitly given automorphisms generated by the maps described above, and let $\operatorname{Aut}(\mathbb{H})$ be the full automorphism group of $\mathbb{H}$. Biswas–Pal–Tomar's rigidity conjecture.

$$G(\mathbb{H}) = \operatorname{Aut}(\mathbb{H}).$$

This conjecture asserts that every automorphism of the hexablock is among the explicitly constructed automorphisms. Its status is not established by the supplied source context.