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Symmetry 2015, 7(2), 774-787; doi:10.3390/sym7020774

Flexible Polyhedral Surfaces with Two Flat Poses

Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8-10/104, 1040 Wien, Austria
Academic Editor: Bernd Schulze
Received: 3 April 2015 / Revised: 19 May 2015 / Accepted: 19 May 2015 / Published: 27 May 2015
(This article belongs to the Special Issue Rigidity and Symmetry)
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Abstract

We present three types of polyhedral surfaces, which are continuously flexible and have not only an initial pose, where all faces are coplanar, but pass during their self-motion through another pose with coplanar faces (“flat pose”). These surfaces are examples of so-called rigid origami, since we only admit exact flexions, i.e., each face remains rigid during the motion; only the dihedral angles vary. We analyze the geometry behind Miura-ori and address Kokotsakis’ example of a flexible tessellation with the particular case of a cyclic quadrangle. Finally, we recall Bricard’s octahedra of Type 3 and their relation to strophoids. View Full-Text
Keywords: flexible polyhedral surface; Miura-ori; Kokotsakis mesh; Kokotsakis tessellation; Bricard octahedron of Type 3; paper folding; strophoid flexible polyhedral surface; Miura-ori; Kokotsakis mesh; Kokotsakis tessellation; Bricard octahedron of Type 3; paper folding; strophoid
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Stachel, H. Flexible Polyhedral Surfaces with Two Flat Poses. Symmetry 2015, 7, 774-787.

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