Illinois Journal of Mathematics

Flexible suspensions with a hexagonal equator

Victor Alexandrov and Robert Connelly

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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.

Article information

Illinois J. Math., Volume 55, Number 1 (2011), 127-155.

First available in Project Euclid: 19 December 2012

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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.

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