Abstract
A new type of hinging is explored for geometric dissections of two-dimensional figures. The figures are represented by pieces on two adjacent levels. Piano hinges are used to rotate a piece B from being next to a piece A on one level to being above or below piece A on another level. Techniques are presented and analyzed for designing piano-hinged dissections. These include the use of polygon structure, the conversion from twisted-hinged dissections, the folding analogue of a P-slide, the folding analogue of a step dissection, and the use of tessellations. Properties of piano-hinged dissections are explored. An open problem relating to the possible universality of such hingings is posed.
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Frederickson, G.N. (2003). Piano-Hinged Dissections: Now Let’s Fold!. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_16
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DOI: https://doi.org/10.1007/978-3-540-44400-8_16
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