Some polycubes have no edge-unzipping.
E. Demaine,
M. Demaine,
D. Eppstein, and
J. O'Rourke.
arXiv:1907.08433.
Proc. 32nd Canadian Conference on Computational Geometry, 2020, pp. 101–105.
Geombinatorics 31 (3): 101–109, 2022.
We find polycubes that cannot be cut along a simple path through their vertices and edges and unfolded to form a flat polygon in the plane.
(CCCG'20 talk video by O'Rourke – Blog post: A zipless polycube)