Paper by Erik D. Demaine

Reference:

Klara Mundilova, Erik D. Demaine, Robert J. Lang, and Tomohiro Tachi, “Analysis of Huffman's Hexagonal Column with Cusps”, in Origami⁸: Proceedings of the 8th International Meeting on Origami in Science, Mathematics and Education (OSME 2024), Melbourne, Australia, July 16–18, 2024, to appear.

Abstract:

We analyze the mathematical existence of one of David Huffman's most prominent curved-crease designs: the Hexagonal Column with Cusps, featuring circular, parabolic, and straight creases. Observations of the physical folded shape suggest that the concave regions between two parabolas form a cylinder, and the regions between the circle and the nearest intersection of the parabolas form a cone. In our analysis, we deduce the remaining rulings that result in a numerically closed hexagonal shape. Finally, we explore other variations of the shape, including those that incorporate only circular creases.

Length:

The paper is 16 pages.

Availability:

The paper is available in PDF (2399k).

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