Access the full text.
Sign up today, get DeepDyve free for 14 days.
(2018)
pages 63–83
(2011)
Illinois J
Georg Grasegger, Jan Legerský, J. Schicho (2017)
Graphs with Flexible LabelingsDiscrete & Computational Geometry
R. Connelly (1975)
An attack on rigidity. I, IIBulletin of the American Mathematical Society, 81
Italy Email address: mgallet@sissa.it
Gallet M. (2021)
7C. R. Math., 359
Chern, Shiing-Shen (2007)
L’Enseignement Mathématique
N. Kuiper (1979)
Sphères Polyédriques Flexibles dans E3, d’après Robert Connelly
Alexandrov V. (2019)
11J. Geom., 110
(2021)
SIAM Journal on Discrete Mathematics
H. Gluck (1975)
Almost all simply connected closed surfaces are rigid
R. Bricard
Mémoire sur la théorie de l'octaèdre articuléJournal de Mathématiques Pures et Appliquées, 3
N. Kuiper (1978)
Sphères polyédriques flexibles dans $E^3$, 20
V. Alexandrov, R. Connelly (2009)
Flexible suspensions with a hexagonal equatorIllinois Journal of Mathematics, 55
Matteo Gallet, Georg Grasegger, Jan Legerský, J. Schicho (2019)
On the existence of paradoxical motions of generically rigid graphs on the sphereArXiv, abs/1908.00467
V. Alexandrov (2018)
A sufficient condition for a polyhedron to be rigidJournal of Geometry, 110
M. Ghomi (2017)
OPEN PROBLEMS IN GEOMETRY OF CURVES AND SURFACES
Bricard R. (1897)
113J. Math. Pures Appl., 3
(2001)
Some necessary metric conditions for the flexibility of suspensions
(1979)
Kuiper . Sphères polyédriques flexibles dans E 3 , d ’ après Robert Connelly
binatorics of Bricard ’ s octahedra
(2001)
3):15–21
(2001)
Mikhalëv, Some necessary metric conditions for the flexibility of suspensions
R. Connelly (1977)
A counterexample to the rigidity conjecture for polyhedraPublications Mathématiques de l'Institut des Hautes Études Scientifiques, 47
Austrian Academy of Sciences Email address: georg.grasegger@ricam.oeaw.ac.at (JL, JS)
(2020)
and Josef Schicho
V. Alexandrov (2019)
Necessary conditions for the extendibility of a first-order flex of a polyhedron to its flexBeiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 61
(1967)
Octaèdres articulés de Bricard
Cauchy A. (1813)
66J. Éc. polytech., 9
Gaifullin A. A. (2018)
63
Numérisation mathématiques (1959)
Publications mathématiques de l'IHES
(1975)
An attack on rigidity I
A. Cauchy (2009)
Recherches sur les polyèdres (Premier Mémoire)
(1975)
An abridged version: R. Connelly, An attack on rigidity
(1975)
In Geometric topology (Proc
(2019)
Discrete & Computational Geometry
(2019)
110(2):Paper No
Connelly R. (1975)
1
Matteo Gallet, Georg Grasegger, Jan Legerský, J. Schicho (2020)
Combinatorics of Bricard’s octahedraComptes Rendus. Mathématique
(2020)
Beitr
A. Gaifullin (2016)
Flexible Polyhedra and Their VolumesarXiv: Metric Geometry
We show that if a polyhedron in the three‐dimensional affine space with triangular faces is flexible, that is, 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 weighted by 1 and −1$-1$. We do this via elementary combinatorial considerations, made possible by a well‐known compactification of the three‐dimensional affine space as a quadric in the four‐dimensional projective space. The compactification is related to the Euclidean metric, and allows us to use a simple degeneration technique that reduces the problem to its one‐dimensional analog, which is trivial to solve.
Bulletin of the London Mathematical Society – Wiley
Published: Feb 1, 2022
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.