2011/01/01 by Victor Alexandrov, Robert Connelly · 7 citations
Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Mathematics #Polyhedron #Combinatorics #Conjecture #Bounded function #Invariant (physics) #Suspension (topology) #Euclidean geometry #Hexagonal crystal system #Euclidean space #Equator #Space (punctuation) #Bellows #Mathematical analysis #Pure mathematics #Geometry #Crystallography #Mathematical physics #Homotopy #Physics
paper · pdf · doi:10.1215/ijm/1355927031
published in Illinois Journal of Mathematics 55(1) (Duke University Press)
openalex publication_date 2011/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct a flexible (non-embedded) suspension with a hexagonal equator in Euclidean 3-space. It is known that the volume bounded by such a suspension is well defined and constant during the flex. We study its properties related to the Strong Bellows Conjecture which reads as follows: if a, possibly singular, polyhedron \mathcal P in Euclidean 3-space is obtained from another, possibly singular, polyhedron \mathcal Q by a continuous flex, then \mathcal P and \mathcal Q have the same Dehn invariants. It is well known that if \mathcal P and \mathcal Q are embedded, with the same volume and the same Dehn invariant, then they are scissors congruent.