# Some Unistable Polyhedra

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A polyhedral solid with uniform density is unistable (or monostable) if it is stable on exactly one face. Besides these polyhedra, this Demonstration also considers polyhedra as surfaces, skeletons, and as a set of vertices.

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Contributed by: Izidor Hafner (June 2014)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

A face of a polyhedron is stable if and only if the orthogonal projection of the center of mass onto the face lies inside the face or on the edge [1, p. 273].

References

[1] J. Bryant and C. Sangwin, *How Round Is Your Circle?: Where Engineering and Mathematics Meet*, Princeton: Princeton University Press, 2008 pp. 273–276.

[2] R. K. Guy, *A Unistable Polyhedron*, Calgary: University of Calgary Department of Mathematics, 1968.

[3] J. H. Conway, M. Goldberg, and R. K. Guy, Problem 66-12, *SIAM Review* 11, 1969 pp. 78–82.

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