Coning, symmetry, and spherical frameworks

Schulze, Bernd and Whiteley, Walter (2012) Coning, symmetry, and spherical frameworks. Discrete and Computational Geometry, 48 (3). pp. 622-657. ISSN 0179-5376

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In this paper, we combine separate works on (a) the transfer of infinitesimal rigidity results from an Euclidean space to the next higher dimension by coning (Whiteley in Topol. Struct. 8:53–70, 1983), (b) the further transfer of these results to spherical space via associated rigidity matrices (Saliola and Whiteley in arXiv:0709.3354, 2007), and (c) the prediction of finite motions from symmetric infinitesimal motions at regular points of the symmetry-derived orbit rigidity matrix (Schulze and Whiteley in Discrete Comput. Geom. 46:561–598, 2011). Each of these techniques is reworked and simplified to apply across several metrics, including the Minkowskian metric Md and the hyperbolic metric ℍ d . This leads to a set of new results transferring infinitesimal and finite motions associated with corresponding symmetric frameworks among Ed , cones in Ed+1 , Sd , Md , and ℍ d . We also consider the further extensions associated with the other Cayley–Klein geometries overlaid on the shared underlying projective geometry.

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Journal Article
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Discrete and Computational Geometry
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24 Apr 2013 09:05
Last Modified:
20 Sep 2023 00:28