On flexible polyhedral surfaces
type: Item
instance of: scholarly article
title: On flexible polyhedral surfaces
zbMATH Open document ID: 1357.52021
DOI: 10.1134/S0081543815010125
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2015-08-20T00:00:00Z
review text: A polyhedral 2-dimensional surface in Euclidean 3-space is said to be flexible if its spatial shape can be changed continuously due to changes of its dihedral angles only, i.\,e., if every face remains self-congruent during this deformation. The deformation is called a flex. The author constructs a closed orientable polyhedral surface of arbitrary genus that is embedded in Euclidean 3-space and admits a one-parameter flex under which all its handles change their shape. This surface admits no other flexes. The author also constructs a flexible closed nonorientable polyhedral surface of arbitrary genus such that all its handles and Möbius strips change their shape during the flex.
reviewed by: Victor Alexandrov
Mathematics Subject Classification ID: 52C25
zbMATH DE Number: 6473905
zbMATH Keywords: Cauchy theorem
zbMATH Keywords: polyhedral surface
zbMATH Keywords: quadrangle
zbMATH Keywords: pyramid
author: Mikhail Shtogrin
MaRDI profile type: Publication
cites work: Q5802755
cites work: A new example of a flexible polyhedron
cites work: Q3857362
cites work: Q4110345
cites work: A counterexample to the rigidity conjecture for polyhedra
cites work: The rigidity of certain cabled frameworks and the second-order rigidity of arbitrary triangulated convex surfaces
cites work: Rigidity of zonohedra
cites work: On rigidity of polyhedral spheres with even-angle faces
cites work: Rigidity of a quadrillage of the torus
cites work: Q4076414
cites work: Q4482596
cites work: An attack on rigidity. I, II
cites work: Q3874915
cites work: Q3278734
cites work: Algebraic methods for solution of polyhedra
cites work: Rigidity of a quadrillage of the pretzel
cites work: Bending of a piecewise developable surface
cites work: A flexible disk with a handle
description: scientific article; zbMATH DE number 6473905