Illinois Journal of Mathematics

Flexible suspensions with a hexagonal equator

Victor Alexandrov and Robert Connelly

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Abstract

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

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

Dates
First available in Project Euclid: 19 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1355927031

Mathematical Reviews number (MathSciNet)
MR3006683

Zentralblatt MATH identifier
1259.52014

Subjects
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

Citation

Alexandrov, Victor; Connelly, Robert. Flexible suspensions with a hexagonal equator. Illinois J. Math. 55 (2011), no. 1, 127--155. https://projecteuclid.org/euclid.ijm/1355927031


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