Folding Cowley's Dodecarhombus Net

This Demonstration shows the folding of Cowley's net into a nonconvex solid with polygonal faces. (The viewpoint zooms in as the figure closes.)
In [1, pp. 2–3] and [3, p. 22–23], it was shown that Cowley's dodecarhombus net does not consist of golden rhombuses or of rhombuses of a rhombic dodecahedron, so it cannot be folded into a convex polyhedron. However, it can be folded into a nonconvex polyhedron by introducing additional creases. One solution: by considering Cowley's rhombuses as hinged equilateral triangles, the net can be folded into a nonconvex polyhedron. Thus, in this case, rhombuses are a kind of skeleton in the sense of [4, p. 282], although not all dihedral angles are congruent. See [5, p. 79] for more about Cowley's books.


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[1] "Rombski poliedri." (Jan 7, 2019)
[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, Aonohedra, Monohedra, Isozonohedra and Otherhedra." (Jan 7, 2019)
[4] P. R. Cromwell, Polyhedra, New York: Cambridge University Press, 1997.
[5] M. Friedman, A History of Folding in Mathematics: Mathematizing the Margins, New York, NY: Springer Berlin Heidelberg, 2018.
[6] Wikipedia. "Bilinski Dodecahedron." (Jan 7, 2019)
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