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  • Finite and infinitesimal rigidity with polyhedral norms

    Rights statement: The final publication is available at Springer via http://dx.doi.org/10.1007/s00454-015-9706-x

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  • Finite and infinitesimal rigidity with polyhedral norms

    Rights statement: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

    Final published version, 543 KB, PDF document

    Available under license: CC BY: Creative Commons Attribution 4.0 International License

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Finite and infinitesimal rigidity with polyhedral norms

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>09/2015
<mark>Journal</mark>Discrete and Computational Geometry
Issue number2
Volume54
Number of pages22
Pages (from-to)390-411
Publication StatusPublished
Early online date29/05/15
<mark>Original language</mark>English

Abstract

We characterise finite and infinitesimal rigidity for bar-joint frameworks in Rd with respect to polyhedral norms (i.e. norms with closed unit ball P, a convex d-dimensional polytope). Infinitesimal and continuous rigidity are shown to be equivalent for finite frameworks in Rd which are well-positioned with respect to P. An edge-labelling determined by the facets of the unit ball and placement of the framework is used to characterise infinitesimal rigidity in Rd in terms of monochrome spanning trees. An analogue of Laman’s theorem is obtained for all polyhedral norms on R2.

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Acceptance information is shown on publishers pdf. The final publication is available at Springer via http://dx.doi.org/10.1007/s00454-015-9706-x The publishers version of this article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.