Abstract
Finding necessary conditions for the geometry of flexible polyhedra is a classical problem that has received attention also in recent times. For flexible polyhedra with triangular faces, we showed in a previous work the existence of cycles with a sign assignment for their edges, such that the signed sum of the edge lengths along the cycle is zero. In this work, we extend this result to flexible non-triangular polyhedra.
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Reference
Gallet, M., Grasegger, G., Legerský, J., Schicho, J.: Zero-sum cycles in flexible polyhedra. Bulletin of the London Mathematical Society (2021), accepted for publication; preprint version. arXiv:2009.14041
Acknowledgments
Josef Schicho and Jan Legerský have been supported by the Austrian Science Fund (FWF): P31061. Jan Legerský has been supported by the Ministry of Education, Youth and Sports of the Czech Republic, project no. CZ.02.1.01/0.0/0.0/16_019/0000778. Matteo Gallet has been supported by the Austrian Science Fund (FWF): Erwin Schrödinger Fellowship J4253. Georg Grasegger has been supported by the Austrian Science Fund (FWF): P31888.
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Gallet, M., Grasegger, G., Legerský, J., Schicho, J. (2022). Zero-Sum Cycles in Flexible Non-triangular Polyhedra. In: Holderbaum, W., Selig, J.M. (eds) 2nd IMA Conference on Mathematics of Robotics. IMA 2020. Springer Proceedings in Advanced Robotics, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-030-91352-6_14
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DOI: https://doi.org/10.1007/978-3-030-91352-6_14
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