Nets for Cowley's Dodecarhombus

This Demonstration shows that Cowley's net can be folded into a nonconvex solid with nonplanar faces.
In [1, pp. 2–3], it was shown that Cowley's dodecarhombus net (taken from [3] for this Demonstration) did not consist of golden rhombuses nor of rhombuses of rhombic dodecahedron, so it cannot be folded into a convex polyhedron. But if we consider Cowley's rhombuses as hinged equilateral triangles, his net can be folded into a nonconvex polyhedron. So in this case, rhombuses are a kind of skeleton in the sense of [4, p. 282], although not all dihedral angles are congruent.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

References
[1] "Rombski Poliedri." (Dec 3, 2018) www.logika.si/revija/Stare-revije/revija15-5.pdf.
[2] J. L. Cowley, Geometry Made Easy: A New and Methodical Explanation of the Elemnets [sic] of Geometry, London: Mechell, 1752.
[3] B. Grünbaum. "The Bilinski Dodecahedron, and Assorted Parallelohedra, Zonohedra, Monohedra, Isozonohedra and Otherhedra." (Dec 3, 2018) digital.lib.washington.edu/researchworks/bitstream/handle/1773/15593/Bilinski_dodecahedron.pdf.
[4] P. R. Cromwell, Polyhedra, New York: Cambridge University Press, 1997.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.