Ununfoldable polyhedra with convex faces

Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper, we study the limits of unfoldability by studying nonconvex polyhedra with the same combinatorial structure as convex polyhedra. In particular, we give two examples of polyhedra, one with 24 convex faces and one with 36 triangular faces, that cannot be unfolded by cutting along edges. We further show that such a polyhedron can indeed be unfolded if cuts are allowed to cross faces. Finally, we prove that "open" polyhedra with triangular faces may not be unfoldable no matter how they are cut.

• Publication year

  1999

• Venue

  Computational geometry

• Publication date

  1999-08-03

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1016/S0925-7721(02)00091-3arXiv cs/9908003
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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