# An Unfoldable Polyhedron

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To unfold a polyhedron, cut it along some edges and flatten it out to form a net. (Allowing cuts on faces as well as edges is called a general unfolding.)

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Contributed by: Izidor Hafner (August 2016)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

In [2] a polyhedron that can be edge-unfolded only with overlaps, is called an unfoldable polyhedron. The proof of the unfoldability of the spiked tetrahedron can be found in [2].

References

[1] M. Bern, E. D. Demaine, D. Eppstein and E. Kuo, "Ununfoldable Polyhedra," in *Proceedings of the 11th Canadian Conference on Computational Geometry (CCCG'99)*, Vancouver, 1999 pp. 13-16. www.cccg.ca/proceedings/1999/fp38.pdf.

[2] E. D. Demaine and J. O'Rourke, *Geometric Folding Algorithms: Linkages, Origami, Polyhedra,* New York: Cambridge University Press, 2007, pp. 318–320.

## Permanent Citation

"An Unfoldable Polyhedron"

http://demonstrations.wolfram.com/AnUnfoldablePolyhedron/

Wolfram Demonstrations Project

Published: August 9 2016