When can a net fold to a polyhedron?

Authors:
Therese Biedl;Anna Lubiw;Julie Sun
Affiliations:
School of Computer Science, University of Waterloo, Waterloo, ON, Canada;School of Computer Science, University of Waterloo, Waterloo, ON, Canada;School of Computer Science, University of Waterloo, Waterloo, ON, Canada
Venue:
Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
Year:
2005

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Abstract

In this paper, we study the problem of whether a polyhedron can be obtained from a net by folding along the creases. We show that this problem can be solved in polynomial time if the dihedral angle at each crease is given, and it becomes NP-hard if these angles are unknown. We also study the case when the net has rigid faces that should not intersect during the folding process.