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Journal for Geometry and Graphics 12 (2008), No. 1, 001--010
Copyright Heldermann Verlag 2008

Infinitesimally Flexible Skeleta of Cross-Polytopes and Second-Hypersimplices

Ciprian S. Borcea
Dept. of Mathematics, Rider University, Lawrenceville, NJ 08648, U.S.A.

We study the infinitesimal flexibility of frameworks in Rd with graphs corresponding to the 1-skeleton of a cross-polytope, respectively second-hyper-simplex, of dimension d. Both represent generalizations of the classical case of the octahedron: the former in the regular sense, resulting in 'overbraced' linkages for d ≥ 4, and the latter in the sense of minimally rigid graphs.

Keywords: Linkage, rigidity, infinitesimal flexibility, cross-polytope, second-hyper-simplex.

MSC: 52C25

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