An Unfoldable Polyhedron

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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.)

[more]

This Demonstration shows a "spiked tetrahedron" of Bern et al. [1]. It can only be unfolded with overlaps since one quarter of it (a "hat") can be unfolded only with overlaps.

[less]

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.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send