Journal for Geometry and Graphics 22 (2018), No. 2, 269--281
Copyright Heldermann Verlag 2018
Dual Tiling Origami
Akito Adachi
The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
adachi.akito.53u@gmail.com
Tomohiro Tachi
The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
tachi@idea.c.u-tokyo.ac.jp
Yasushi Yamaguchi
The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
yama@graco.c.u-tokyo.ac.jp
This paper proposes a class of origami, dual tiling origami, which is an extension of Lang's "Octet Truss". Dual tiling origami lies between two parallel planes and tessellates both sides with polygonal tiles. The tiling patterns on both surfaces are dual, and the structure comprises cones of these tiling polygons on both sides with tetrahedra between them. Three conditions for the existence of dual tiling origami are shown. If the folded shape is flat, dual tiling origami can tessellate a family of parallelogram lattices. For the thick case, the relation between parameters of the parallelograms and the height between two planes is discussed. These dual tiling origami can converge to Miura-Ori under a certain condition.
Keywords: Origami tessellation, tiling, core panel.
MSC: 51M20; 53A05, 68U05
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