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arXiv · 0812.3050

On the flexibility of Kokotsakis meshes

Oleg Karpenkov
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Abstract

In this paper we study geometric, algebraic, and computational aspects of flexibility and infinitesimal flexibility of Kokotsakis meshes. A Kokotsakis mesh is a mesh that consists of a face in the middle and a certain band of faces attached to the middle face by its perimeter. In particular any 3x3-mesh made of quadrangles is a Kokotsakis mesh. We express the infinitesimal flexibility condition in terms of Ceva and Menelaus theorems. Further we study semi-algebraic properties of the set of flexible meshes and give equations describing it. For 3x3-meshes we obtain flexibility conditions in terms of face angles.

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Oleg Karpenkov. 2008-12-16. On the flexibility of Kokotsakis meshes. https://arxiv.org/abs/0812.3050

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