Maximum Inscribed Convex Body in a Non-Convex Polytope

Determine the maximum-volume convex body, or more generally the maximum-volume convex polyhedron, inscribed in a non-convex polytope, thereby replacing the axis-aligned rectangular-prism core used by Print with a more general convex core and potentially improving volume efficiency for non-box-like 3D models.

Background

Print currently seeks a maximum-volume axis-aligned rectangular prism contained within a complex 3D mesh. The rectangular prism provides six orthogonal faces that support the algorithm’s overlap-free unfolding strategy, but it can yield poor volume efficiency for thin-shelled, concave, or strongly varying models.

The paper identifies finding the largest inscribed convex body in a non-convex polytope as related to the open Convex Skull Problem. In the Discussion, the authors describe replacing the rectangular prism with a maximum inscribed convex polyhedron as a natural extension that could generalize the method to arbitrary convex cores and increase the hollow volume for non-box-like models.

References

Finding the largest inscribed convex body in a non-convex polytope is related to the open Convex Skull Problem, so next we adopt a two-phase heuristic.

— Print&Fold: Printing and Folding Shape-accurate 3D Models  (2608.13279 - Kumar et al., 13 Aug 2026) in Section 4, “Print Technical Pipeline,” subsection “Complex 3D Meshes,” Step 1 — Maximum inscribed rectangular prism; discussed again in Section 6, “Discussion,” under “Limitations”