Necessary conditions for the extendibility of a first-order flex of a polyhedron to its flex

Abstract

We derive fundamentally new equations that are satisfied by first-order flexes of a flexible polyhedron. Moreover, we indicate two sources of such new equations. These sources are the Dehn invariants and rigidity matrix. The equations derived provide us with fundamentally new necessary conditions for the extendibility of a first-order flex of a polyhedron to its flex.

12 pages, 2 figures

References in corpus (2)

• Dehn invariant of flexible polyhedra
• A sufficient condition for a polyhedron to be rigid

Cited by in corpus (2)

• Zero-sum cycles in flexible polyhedra
• A note on the first-order flexes of smooth surfaces which are tangent to the set of all nonrigid surfaces