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Journal for Geometry and Graphics 14 (2010), No. 2, 147--169
Copyright Heldermann Verlag 2010

Flexible Octahedra in the Projective Extension of the Euclidean 3-Space

Georg Nawratil
Inst. of Discrete Mathematics and Geometry, University of Technology, Wiedner Hauptstr. 8-10/104, 1230 Vienna, Austria

We complete the classification of flexible octahedra in the projective extension of the Euclidean 3-space. If all vertices are Euclidean points then we get the well known Bricard octahedra. All flexible octahedra with one vertex on the plane at infinity were already determined by the author in the context of self-motions of TSSM manipulators with two parallel rotary axes. Therefore we are only interested in those cases where at least two vertices are ideal points. Our approach is based on Kokotsakis meshes and reducible compositions of two four-bar linkages.

Keywords: Flexible octahedra, Kokotsakis meshes, Bricard octahedra.

MSC: 53A17; 52B10

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