Tilings and patterns
Dudeney Dissection of Polygons
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
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Two ways of hinging geometric dissections of 2-dimensional figures are explored. Swing hinges allow rotation in the plane. Twist hinges allow rotation by 180掳 through the third dimension. Techniques are presented and analyzed for designing hingeable dissections that use either only swing hinges or only twist hinges. For swing hinges these include the superposition of tessellations, the crossposition of T-strips, and the exploitation of the structure of regular polygons and stars. For twist hinges these include the conversion of swing hinges, the P-twist for parallelograms, and completing the pseudo-tessellation. Open problems relating to the possible universality of such hingings are posed.