Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 55, Number 1 (2011), 127-155.
Flexible suspensions with a hexagonal equator
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 in Euclidean 3-space is obtained from another, possibly singular, polyhedron by a continuous flex, then and have the same Dehn invariants. It is well known that if and are embedded, with the same volume and the same Dehn invariant, then they are scissors congruent.
Illinois J. Math., Volume 55, Number 1 (2011), 127-155.
First available in Project Euclid: 19 December 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 52C25: Rigidity and flexibility of structures [See also 70B15]
Secondary: 51M20: Polyhedra and polytopes; regular figures, division of spaces [See also 51F15] 14H50: Plane and space curves
Alexandrov, Victor; Connelly, Robert. Flexible suspensions with a hexagonal equator. Illinois J. Math. 55 (2011), no. 1, 127--155. doi:10.1215/ijm/1355927031. https://projecteuclid.org/euclid.ijm/1355927031