Abstract
Background of our talk is tessellabilities, reversibilities, and decomposabilities of polygons, polyhedra, and polytopes, where by the word “tessellability”, we mean the capability of the polytope to tessellate. Although these three concepts seem quite different, but there is a strong connection linking them. These connections will be shown when we consider the lattices of tilings in ℝ2 and tessellations in ℝ3. In this talk, we mainly discuss reversibilties of polygons from the standpoint of algorithm. We give an algorithm to check whether a given pair of polygons α and β with the same area is reversible or not. Many old and new results together with various research problems relating this topic will be presented.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Bolyai, F.: Tentamen juventutem. Marcos Vasarhelyini: Typis Collegii Refomatorum per Josephum et Simeonem Kali (1832) (in Latin)
Gerwien, P.: Zerschneidung jeder bliebigen Anzahl von gleichen geradlinigen Figuren in dieselben Stücke. Journal für die reine und angewandte Mathematik (Crelle’s Journal) 10, 228–234 and Taf. III
Hilbert, D.: Mathematische Probleme. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse. Subsequently in Bulletin of the American Mathematical Society 8, 437–479 (1901-1902)
Dehn, M.: Über den Rauminhalt, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 345-54. Subsequently in Mathematische Annalen 55(3), 465–478 (1902)
Dudeney, H.: The Canterbury Puzzles. Thomas Nelson and Sons (1907)
Boltyanskii, V.G.: Equivalent and Equidecomposable Figures, D. C. Health and Co. (1963), Henn, A.K., Watts, C.E., Translated and adapted from the first Russian edition (1956)
Boltyanskii, V.G.: Hilbert’s Third Problem, V. H. Winston and Sons. In: Silverman, A., Translated by from the first Russian edition (1978)
Akiyama, J., Nakamura, G.: Congruent dissections of triangles and quadrilaterals - All the hinge points are on the sides of the polygon. In: Aronov, B., Basu, S., Pach, J., Sharir, M. (eds.) Discrete and Computational Geometry, The Goodman-Pollak Festschrift. Algorithms and Combinatorics, pp. 43–63. Springer (2003)
Akiyama, J., Sato, I., Seong, H.: On reversibility among parallelohedra. In: Márquez, A., Ramos, P., Urrutia, J. (eds.) EGC 2011. LNCS, vol. 7579, pp. 14–28. Springer, Heidelberg (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Akiyama, J., Seong, H. (2013). An Algorithm for Determining Whether a Pair of Polygons Is Reversible. In: Fellows, M., Tan, X., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7924. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38756-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-38756-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38755-5
Online ISBN: 978-3-642-38756-2
eBook Packages: Computer ScienceComputer Science (R0)