Nonflexible polyhedra with a small number of vertices
type: Item
instance of: scholarly article
title: Nonflexible polyhedra with a small number of vertices
zbMATH Open document ID: 1179.52029
author: I. G. Maksimov
published in: Journal of Mathematical Sciences (New York)
publication date: 2008-10-28T00:00:00Z
review text: The minimal number of vertices of an embedded or immersed, flexible polyhedral surface in three dimension is still unknown. By considering all combinatorial types of polyhedral surfaces with at most \(8\) vertices, the author shows that this number is either \(7\) or \(8\). It is moreover shown that a flexible polyhedral surface with \(8\) vertices would have to be of one specific combinatorial type. An example with nine vertices was previously known by work of Steffen (1978).
Mathematics Subject Classification ID: 52C25
zbMATH DE Number: 5358132
zbMATH Keywords: nonflexible polyhedra
zbMATH Keywords: embedded
zbMATH Keywords: immersed
MaRDI profile type: Publication
full work available at URL: s10958-008-0037-9
OpenAlex ID: W2056275608
cites work: Generation of Triangulations of the Sphere
cites work: A counterexample to the rigidity conjecture for polyhedra
cites work: Suspensions: Volumes, immersibility, and rigidity
cites work: Q3766407
cites work: Q3496859
DOI: 10.1007/S10958-008-0037-9
description: scientific article; zbMATH DE number 5358132