Dissection of Half an Obtuse Golden Rhombohedron and Half an Acute Golden Rhombohedron into a Cube

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This Demonstration shows a dissection of a half of an obtuse golden rhombohedron and a half of an acute golden rhombohedron into a cube.

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For a volume of the obtuse golden rhombohedron of , the volume of the acute golden rhombohedron equals , where is the golden ratio. Thus this Demonstration implies the identity . Note that can be replaced by in this identity: .

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Contributed by: Izidor Hafner and Mateja Budin (September 2019)
Open content licensed under CC BY-NC-SA


Details

References

[1] W. W. R. Ball and H. S. M. Coxeter, Mathematical Recreations and Essays, 13th ed., New York: Dover Publications, 1987 p. 161.

[2] I. Hafner and M. Budin, "Dissection of Cubes and Golden Rhombic Solids," in Aproged's 5th International Conference, Geometrias '19: Polyhedra and Beyond, Porto, Portugal (V. Viana, ed.), Porto: Aproged, 2019 pp. 91–93. www.aproged.pt/geometrias19proceedings.html.


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