Work

Unfolding Solid Polycubes

Year: 2026

Type: article

Abstract: A solid polycube is a face-connected set of unit cubes, where, unlike classical definitions for polycubes, shared faces between adjacent cubes are not removed. We prove by mathematical induction that any such polycube can be edge-unfolded into a 2D net without refinement. Our proof relies on the concept of a perfect net, defined as a net in which two designated edges are placed on the far left and far right sides. This configuration enables consistent gluing of nets in a single direction throughout the induction process, thereby guaranteeing that no overlaps occur at any step.

Source: Discrete Mathematics & Theoretical Computer Science

DOI: 10.46298/dmtcs.16116

Authors: Bastien Harismendy, Tom da Silva, Gaëlle Largeteau-Skapin, Éric Andrès

Institutions: Université de Poitiers, Centre National de la Recherche Scientifique, XLIM, Université de Limoges

Language: English

Topic: Computational Geometry and Mesh Generation

Subfield: Computer Graphics and Computer-Aided Design

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4414699282

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