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Geometric Dissections that Swing and Twist

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Discrete and Computational Geometry (JCDCG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2098))

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Abstract

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° through the third dimension. Techniques are presented and analyzed for designing hingeable dissections that use either only swings 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-tesellation. Open problems relating to the possible universality of such hingings are posed.

Supported in part by the National Science Foundation under grant CCR-9731758.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Purdue University, West Lafayette, IN, 47907, USA

    Greg N. Frederickson

Authors
  1. Greg N. Frederickson
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Editor information

Editors and Affiliations

  1. Research Institute of Educational Development, Tokai University, 2-28-4 Tomigaya, Shibuya-ku, Tokyo, 151-0063, Japan

    Jin Akiyama

  2. Department of Computer and Information Sciences, Ibaraki University, Hitachi, 316-8511, Japan

    Mikio Kano

  3. Department of Mathematics, Tokai University, 3-20-1 Orido Shimizu-shi, Shizuoka, 424-8610, Japan

    Masatsugu Urabe

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© 2001 Springer-Verlag Berlin Heidelberg

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Frederickson, G.N. (2001). Geometric Dissections that Swing and Twist. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_11

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  • DOI: https://doi.org/10.1007/3-540-47738-1_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42306-5

  • Online ISBN: 978-3-540-47738-9

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