Geodesic
On flexible polyhedral surfaces
Informatics and Automation, Geometry, topology, and applications, Tome 288 (2015), pp. 171-183.

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We construct a closed orientable polyhedral surface of arbitrary genus that is embedded in three-dimensional Euclidean space and admits a one-parameter bending under which all its handles bend. This surface admits no other bendings. We also construct a flexible closed nonorientable polyhedral surface of arbitrary genus such that all its handles and Möbius strips bend during its bending. 
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M. I. Shtogrin. On flexible polyhedral surfaces. Informatics and Automation, Geometry, topology, and applications, Tome 288 (2015), pp. 171-183. http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a11/

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