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pro vyhledávání: '"Legerský, Jan"'
Steffen's polyhedron was believed to have the least number of vertices among polyhedra that can flex without self-intersections. Maksimov clarified that the pentagonal bipyramid with one face subdivided into three is the only polyhedron with fewer ve
Externí odkaz:
http://arxiv.org/abs/2410.13811
Publikováno v:
Comptes Rendus. Mathématique, Vol 359, Iss 1, Pp 7-38 (2021)
We re-prove the classification of motions of an octahedron — obtained by Bricard at the beginning of the XX century — by means of combinatorial objects satisfying some elementary rules. The explanations of these rules rely on the use of a well-kn
Externí odkaz:
https://doaj.org/article/5f519a8f95d64bde8e704814b90700fb
We study reflection-symmetric realisations of symmetric graphs in the plane that allow a continuous symmetry and edge-length preserving deformation. To do so, we identify a necessary combinatorial condition on graphs with reflection-symmetric flexibl
Externí odkaz:
http://arxiv.org/abs/2408.06928
Autor:
Grasegger, Georg, Legerský, Jan
Publikováno v:
Computational Geometry (2024). 120: Art. 102055
A framework, which is a (possibly infinite) graph with a realization of its vertices in the plane, is called flexible if it can be continuously deformed while preserving the edge lengths. We focus on flexibility of frameworks in which 4-cycles form p
Externí odkaz:
http://arxiv.org/abs/2305.01570
Autor:
Dewar, Sean, Legerský, Jan
Publikováno v:
Discrete Applied Mathematics. 324:1--17, 2023
A planar framework -- a graph together with a map of its vertices to the plane -- is flexible if it allows a continuous deformation preserving the distances between adjacent vertices. Extending a recent previous result, we prove that a connected grap
Externí odkaz:
http://arxiv.org/abs/2110.01854
Autor:
Grasegger, Georg, Legerský, Jan
Publikováno v:
In Computational Geometry: Theory and Applications June 2024 120
Publikováno v:
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 (2022)
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 sig
Externí odkaz:
http://arxiv.org/abs/2108.08744
Publikováno v:
Bulletin of the London Mathematical Society (2022). 54(1):112-125
We show that if a polyhedron in the three-dimensional affine space with triangular faces is flexible, i.e., can be continuously deformed preserving the shape of its faces, then there is a cycle of edges whose lengths sum up to zero once suitably weig
Externí odkaz:
http://arxiv.org/abs/2009.14041
Autor:
Grasegger, Georg, Legerský, Jan
A rectangle in the plane can be continuously deformed preserving its edge lengths, but adding a diagonal brace prevents such a deformation. Bolker and Crapo characterized combinatorially which choices of braces make a grid of squares infinitesimally
Externí odkaz:
http://arxiv.org/abs/2008.11521
Publikováno v:
Comptes Rendus. Math\'ematique, Tome 359 (2021) no. 1, pp. 7-38
We re-prove the classification of flexible octahedra, obtained by Bricard at the beginning of the XX century, by means of combinatorial objects satisfying some elementary rules. The explanations of these rules rely on the use of a well-known creation
Externí odkaz:
http://arxiv.org/abs/2004.01236