# Kepler's Rhombic Triacontahedron and Rhombic Icosahedron

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Kepler made a systemic study of polyhedra beyond the ones defined by Archimedes. Among those were the rhombic icosahedron and the rhombic triacontahedron, which he used in *Harmonices Mundi*.

Contributed by: Izidor Hafner (January 2019)

Open content licensed under CC BY-NC-SA

## Details

A part of an illustration from Kepler's *Harmonices Mundi* (taken from [4] for this Demonstration, also [5, p. 79]) suggests that Kepler was aware of the rhombic icosahedron; its discovery is attributed to Fedorov [2, p. 156].

References

[1] B. Grünbaum. "The Bilinski Dodecahedron, and Assorted Parallelohedra, Aonohedra, Monohedra, Isozonohedra and Otherhedra." (Jan 7, 2019) digital.lib.washington.edu/researchworks/bitstream/handle/1773/15593/Bilinski_dodecahedron.pdf.

[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 Berlin Heidelberg, 2018.

[4] S. Wolfram. "The Story of Spikey" from *Wolfram Blog*—A Wolfram Web Resource. (Jan 7, 2019) blog.wolfram.com/2018/12/28/the-story-of-spikey.

[5] J. Kepler, *Harmonices Mundi*, 1619. (Jan 7, 2019) archive.org/details/ioanniskepplerih00kepl/page/n79.

## Snapshots

## Permanent Citation