Extending polycube refolding to avoid self-intersection and to non-tree shapes

Develop refolding procedures for polycubes that (i) avoid self-intersection without assuming well-separation and (ii) support non-tree-shaped polycubes of the same surface area.

Background

The paper’s polycube algorithm ensures intermediate manifolds are tree-shaped n-cubes and avoids self-intersection only under a well-separation assumption.

Removing these restrictions—both the well-separation requirement and the tree-shaped assumption—would significantly broaden the applicability of the polycube refolding framework.