Folding Nets for Some Golden Rhombic Solids

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This Demonstration shows nets for some golden rhombic solids. The viewpoint changes as the net closes.

Contributed by: Izidor Hafner (February 2019)
Open content licensed under CC BY-NC-SA


Details

The diagonals of length and in a golden rhombus are in the ratio , where is the golden ratio. The faces of the acute golden rhombohedron, Bilinski dodecahedron, obtuse golden rhombohedron, rhombic icosahedron and rhombic triacontahedron are all golden rhombi [1]. These are the only convex solids that have golden rhombic faces [2, pp. 151–156].

Find more on nets in [3]. For more about nonconvex golden rhombic solids see [4, 5] .

References

[1] E. W. Weisstein. "Golden Rhombus" from Wolfram MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/GoldenRhombus.html (Wolfram MathWorld).

[2] P. R. Cromwell, Polyhedra, New York: Cambridge University Press, 1997.

[3] M. Friedman, A History of Folding in Mathematics: Mathematizing the Margins, New York, NY: Springer International Publishing, 2018.

[4] I. Hafner and T. Zitko. "Introduction to Golden Rhombic Polyhedra." (Feb 18, 2019) www.mi.sanu.ac.rs/vismath/hafner2/IntrodRhombic.html.

[5] I. Hafner and D. Felda. "Rhombic Polyhedra" (in Slovenian). (Feb 18, 2019) www.logika.si/poliedriCDsl/Zlati_rombski_poliedri.pdf.


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