Paper by Martin L. Demaine

Reference:

Eli Davis, Erik D. Demaine, Martin L. Demaine, and Jennifer Ramseyer, “Weaving a Uniformly Thick Sheet from Rectangles”, in Origami⁶: Proceedings of the 6th International Meeting on Origami in Science, Mathematics and Education (OSME 2014), Tokyo, Japan, August 10–13, 2014, pages 177–188, American Mathematical Society.

Abstract:

In this paper, we demonstrate a way to weave together finite-length strips into a uniformly thick infinite sheet. Because we require our sheet to be locked and unable to slip, our model requires more layers than a conventional weave. For an arbitrary rectangle, the sheet is at most 16 layers thick. For some families of tileable shapes, the sheet is at most 18 layers thick. Certain specially designed shapes achieve thinner weaves. We have also designed finite weaves of rectangles that remain locked and uniformly thick, but at the cost of doubling the number of layers

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