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On Geometric Graphs on Point Sets in the Plane Read chapter Read first chapter

2021 | OriginalPaper | Chapter

Crystallographic Flat Origami from n-Uniform Tilings

Authors : Ma. Louise Antonette N. De Las Peñas, Eduard C. Taganap

Published in: Discrete and Computational Geometry, Graphs, and Games

Publisher: Springer International Publishing

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Abstract

This paper discusses the symmetry properties of crystallographic flat origami arising from n-uniform tilings using the hinged tiling method. A flat origami invariant under a plane crystallographic group is called a crystallographic flat origami. An n-uniform tiling is a tiling consisting of regular polygons, with the property that its vertices form n transitivity classes under the action of its symmetry group.

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previous chapter Toward Unfolding Doubly Covered n-Stars
next chapter Packing Cube Nets into Rectangles with O(1) Holes
Literature
1.
Bateman, A.: Computer tools and algorithms for origami tessellation design. In: Hull, T. (ed.) Origami\(^3\): Third International Meeting of Origami Science, Math, and Education, pp. 121–127. CRC Press, Florida (2002)
2.
Bern, M., Hayes, B.: The complexity of flat origami. In: Proceedings of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 175–183. Atlanta, Georgia (1996)
3.
De Las Peñas, M. L. A., Taganap, E., Rapanut, T.: Color symmetry approach to the construction of crystallographic flat origami. In: Miura, K., et al. (eds.) Origami 6: I. Mathematics, pp. 11–20 (2015)
4.
5.
Hahn, T. (ed.): International tables for crystallography, Vol. A, Space-Group Symmetry, 5th ed. Springer, Heidelberg (2005)
6.
7.
8.
Justin, J.: Toward a mathematical theory of origami. In: Miura, K. (ed.) Origami Science and Art: Proceedings of the Second International Meeting of Origami Science and Scientific Origami, pp. 15–29, Seian University of Art and Design, Otsu, Japan (1997)
9.
Kawasaki, T.: On the relation between mountain-creases and valley-creases of a flat origami (abridged English translation) In: Huzita, H. (ed.) Proceedings of the First International Meeting of Origami Science and Technology, pp. 229–237. Ferrara, Italy (1989)
10.
Kawasaki, T.: Roses, Origami & Math. Japan Publications, Tokyo, Japan (2005)
11.
Kawasaki, T., Yoshida, M.: Crystallographic flat origamis. Mem. Fac. Sci. Kyushu Univ. Ser. A 42(2), 153–157 (1988)
12.
Kasahara, K.: Origami Omnibus, p. 96. Japan Publications, Tokyo, Japan (1988)
13.
Kasahara, K., Takahama, T.: Origami for the Connoisseur, p. 29. Japan Publications, Tokyo (1987)
14.
Lang, R.: Twists, Tilings and Tessellations: Mathematical Methods for Geometric Origami, pp. 236, 287. CRC Press, Florida, USA (2018)
15.
Lang, R., Bateman, A.: Every spider web has a simple flat twist tessellation. In: Wang-Iverson, P., et al. (eds.) Origami\(^5\) : Fifth International Meeting of Origami Science. Mathematics and Education, pp. 455–474. CRC Press, Florida (2010)
16.
Maekawa, J.: The definition of Iso-Area folding. In: Hull, T. (ed.) Origami\(^3\): Proceedings of the Third International Meeting on Origami Science, Mathematics and Education, pp. 53–58. A.K. Peters Ltd., Natick, MA (2002)
17.
Sales, R.E.R.: On the Crystallographic Flat Origami. Ph.D. Dissertation, University of the Philippines Diliman, October 2000
18.
Say-awen, A. L., De Las Peñas, M. L. A., Rapanut, T.: On color fixing groups associated with colored symmetrical tilings. In: Proceedings of the 3rd International Conference on Mathematical Sciences, pp. 050012-1-050012–10 (2014)
19.
Taganap, E., De Las Peñas, M. L. A., Rapanut, T.: Crystallographic flat origami with three flat foldability types of the generating unit. In: Proceedings of the 3rd International Conference on Mathematical Sciences, pp. 662–667 (2014)
20.
Verrill, H.: Origami tessellations. In: Sarhangi, R. (ed.) Conference Proceedings of Bridges: Mathematical Connections in Art, Music and Science, pp. 55–68 (1998)
21.
Wang-Iverson, P., Lang, R., Yang, M. (eds.): Origami\(^5\): Fifth International Meeting of Origami Science. Mathematics and Education, pp. 455–474. CRC Press, Florida (2010)
Metadata
Title
Crystallographic Flat Origami from n-Uniform Tilings
Authors
Ma. Louise Antonette N. De Las Peñas
Eduard C. Taganap
Copyright Year
2021
Book
Discrete and Computational Geometry, Graphs, and Games

Print ISBN: 978-3-030-90047-2

Electronic ISBN: 978-3-030-90048-9

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-90048-9_11