Pseudo-automorphisms of rational threefolds and Kummer surfaces

Kummer surfaces are special quartic surfaces that admit $16$ nodes. The automorphisms of K3 Kummer surfaces are rich and complicated. Based on the results of Keum and Kond\=o, and as a continuation of the recent result by He and Yang, we lift $45$ classically known automorphisms of Kummer surfaces to pseudo-automorphisms of a threefold, the blow-up of $\mathbb{P}^3$ along $6$ points and $15$ lines. We give a description of a fundamental domain of the group generated by all the known pseudo-automorphisms on this threefold.