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Parametrized Goldberg's Tristable Polyhedron with 12 Faces

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This Demonstration shows a parametrized Goldberg's tristable polyhedron where the faces are 12 isosceles triangles. The apex angle of Goldberg's original construction is slightly more than 103 degrees. A rectangular net is shown for the case of 90 degrees.

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There are two Goldberg tristable polyhedra: the one shown here, which has 12 faces, and the one displayed in the Demonstration linked in the Details, which has 20 faces.

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Contributed by: Izidor Hafner (April 2014)
Open content licensed under CC BY-NC-SA

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References

[1] P. R. Cromwell, Polyhedra, Cambridge: Cambridge University Press, 1997 pp. 222–224.

[2] M. Goldberg, "Unstable Polyhedral Structures," Mathematics Magazine, 51(3), 1978 pp. 165–170. www.jstor.org/stable/2689996.

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