Geometric Strategies in Creating Origami Paper Lampshades: Folding Miura-ori, Yoshimura, and Waterbomb Tessellations
This chapter describes geometric strategies in origami design to create paper lanterns that gleam with the luminous gradations of light. While the design of origami paper lampshades is largely based on origami design, it also presents new challenges due t
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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Background on Paper Lanterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contemporary Origami-Inspired Paper Lampshades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Light, Origami Design, and Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design Parameters and Considerations for Origami Lampshade Design . . . . . . . . . . . . . . . . . . Flat-Foldable Origami Tessellations: Miura, Yoshumura, and Waterbomb Patterns . . . . . . . . . Mathematical Theorems Governing Flat-Foldable Origami Tessellations . . . . . . . . . . . . . . . . . Miura-ori Tessellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Miura-ori and the Bird’s-Foot Vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Folding Miura-ori into Cylindrical Lampshade with Translation Symmetry . . . . . . . . . . . . . Folding Miura-ori into a Lampshade with Rotational Symmetry . . . . . . . . . . . . . . . . . . . . . . Yoshimura Tessellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yoshimura Tessellation and Its Double Bird’s Foot Vertex . . . . . . . . . . . . . . . . . . . . . . . . . . Folding Yoshimura into Cylindrical Lampshade with Translational Symmetry . . . . . . . . . . Folding Yoshimura into a Lampshade with Rotational Symmetry . . . . . . . . . . . . . . . . . . . . . Waterbomb Tessellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Waterbomb Tessellation and Its Vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Folding Waterbomb Tessellation into Cylindrical Lampshade with Translational Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Folding Waterbomb Tessellation into a Lampshade with Rotational Symmetry . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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J. Wu () Eskenazi School of Art, Architecture and Design, Indiana University, Bloomington, IN, USA e-mail: [email protected] © Springer Nature Switzerland AG 2020 B. Sriraman (ed.), Handbook of the Mathematics of the Arts and Sciences, https://doi.org/10.1007/978-3-319-70658-0_102-1
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