Advertisement

Common Nets of a Regular Tetrahedron and Johnson-Zalgaller Solids

  • Ryuhei UeharaEmail author
Chapter
  • 147 Downloads

Abstract

As we already saw in Sects.  4.2 and  4.3, common nets for two (or more) regular polyhedra are tough problems, and we cannot say anything about their existence. On the other hand, as introduced in Sect.  2.3, only for nets of a regular tetrahedron, its beautiful and useful characterization is known as a notion of p2 tiling. Then, what happens if one is limited to a net of a regular tetrahedron and the other is limited to an edge-unfolding of a more general polyhedron? In this chapter, as the latter one, we will investigate “an edge-unfolding of a regular-faced convex polyhedron”.

References

  1. [AHU15]
    Y. Araki, T. Horiyama, R. Uehara, common unfolding of regular tetrahedron and Johnson-Zalgaller solid, in The 9th Workshop on Algorithms and Computation (WALCOM 2015). Lecture Notes in Computer Science, vol. 8973 (2015), pp. 294–305Google Scholar
  2. [AHU16]
    Y. Araki, T. Horiyama, R. Uehara, Common unfolding of regular tetrahedron and Johnson-Zalgaller solid. J. Graph Algorithms Appl. 20(1), 101–114 (2016)Google Scholar
  3. [AKL+11]
    J. Akiyama, T. Kuwata, S. Langerman, K. Okawa, I. Sato, G.C. Shephard, Determination of all tessellation polyhedra with regular polygonal faces, in The 9th International Conference of Computational Geometry, Graphs, and Applications (CGGA 2010). Lecture Notes in Computer Science, vol. 7033 (2011), pp. 1–11Google Scholar
  4. [SB15]
    T. Sasao, J.T. Butler (eds.), Applications of Zero-Suppressed Decision Diagrams (Morgan & Claypool Publishers, 2015)Google Scholar
  5. [MHU19]
    K. Mizunashi, T. Horiyama, R. Uehara, Efficient algorithm for box folding, in The 13th International Conference and Workshop on Algorithms and Computation (WALCOM 2019), Lecture Notes in Computer Science, vol. 11355 (2019), pp.  277–288Google Scholar
  6. [DO07]
    E.D. Demaine, J. O’Rourke, Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Cambridge, 2007)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.JAISTIshikawaJapan

Personalised recommendations