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A sufficient condition for a polyhedron to be rigid. / Alexandrov, Victor.

In: Journal of Geometry, Vol. 110, No. 2, 38, 01.08.2019.

Research output: Contribution to journal › Article › peer-review

Harvard

Alexandrov, V 2019, 'A sufficient condition for a polyhedron to be rigid', Journal of Geometry, vol. 110, no. 2, 38. https://doi.org/10.1007/s00022-019-0492-0

APA

Alexandrov, V. (2019). A sufficient condition for a polyhedron to be rigid. Journal of Geometry, 110(2), [38]. https://doi.org/10.1007/s00022-019-0492-0

Vancouver

Alexandrov V. A sufficient condition for a polyhedron to be rigid. Journal of Geometry. 2019 Aug 1;110(2):38. doi: 10.1007/s00022-019-0492-0

Author

Alexandrov, Victor. / A sufficient condition for a polyhedron to be rigid. In: Journal of Geometry. 2019 ; Vol. 110, No. 2.

BibTeX

@article{a4792e5c1f0e41559ec45134b12dac52,
title = "A sufficient condition for a polyhedron to be rigid",
abstract = "We study oriented connected closed polyhedral surfaces with non-degenerate triangular faces in three-dimensional Euclidean space, calling them polyhedra for short. A polyhedron is called flexible if its spatial shape can be changed continuously by changing its dihedral angles only. We prove that for every flexible polyhedron some integer combination of its dihedral angles remains constant during the flex. The proof is based on a recent result of A. A. Gaifullin and L. S. Ignashchenko.",
keywords = "Bricard octahedron, Dehn invariant, Dihedral angle, Flexible polyhedron, Hamel basis, BELLOWS CONJECTURE, FLEXIBLE POLYHEDRA, CROSS-POLYTOPES, VOLUME, INVARIANT",
author = "Victor Alexandrov",
year = "2019",
month = aug,
day = "1",
doi = "10.1007/s00022-019-0492-0",
language = "English",
volume = "110",
journal = "Journal of Geometry",
issn = "0047-2468",
publisher = "Birkhauser Verlag Basel",
number = "2",

}

RIS

TY - JOUR

T1 - A sufficient condition for a polyhedron to be rigid

AU - Alexandrov, Victor

PY - 2019/8/1

Y1 - 2019/8/1

N2 - We study oriented connected closed polyhedral surfaces with non-degenerate triangular faces in three-dimensional Euclidean space, calling them polyhedra for short. A polyhedron is called flexible if its spatial shape can be changed continuously by changing its dihedral angles only. We prove that for every flexible polyhedron some integer combination of its dihedral angles remains constant during the flex. The proof is based on a recent result of A. A. Gaifullin and L. S. Ignashchenko.

AB - We study oriented connected closed polyhedral surfaces with non-degenerate triangular faces in three-dimensional Euclidean space, calling them polyhedra for short. A polyhedron is called flexible if its spatial shape can be changed continuously by changing its dihedral angles only. We prove that for every flexible polyhedron some integer combination of its dihedral angles remains constant during the flex. The proof is based on a recent result of A. A. Gaifullin and L. S. Ignashchenko.

KW - Bricard octahedron

KW - Dehn invariant

KW - Dihedral angle

KW - Flexible polyhedron

KW - Hamel basis

KW - BELLOWS CONJECTURE

KW - FLEXIBLE POLYHEDRA

KW - CROSS-POLYTOPES

KW - VOLUME

KW - INVARIANT

UR - http://www.scopus.com/inward/record.url?scp=85067584456&partnerID=8YFLogxK

U2 - 10.1007/s00022-019-0492-0

DO - 10.1007/s00022-019-0492-0

M3 - Article

AN - SCOPUS:85067584456

VL - 110

JO - Journal of Geometry

JF - Journal of Geometry

SN - 0047-2468

IS - 2

M1 - 38

ER -

ID: 20642746