Journal
SYMMETRY-BASEL
Volume 7, Issue 2, Pages 774-787Publisher
MDPI AG
DOI: 10.3390/sym7020774
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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.
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