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A tensegrity polygon is a planar cable-strut tensegrity framework in which
the cables form a convex polygon containing all vertices.
The underlying edge-labeled graph,
in which the cable edges form a
Hamilton cycle, is an abstract tensegrity polygon.
It is said to be robust if every convex realization as a tensegrity polygon
has an equilibrium stress which is positive on the cables and negative
on the struts. It is called
stable if every convex realization is infinitesimally rigid.
We characterize the robust as well as
the stable abstract tensegrity polygons on n vertices
with n-2 struts, answering a question of B. Roth and W. Whiteley
from 1981 and solving an open problem of R. Connelly from 2008.
Bibtex entry:
| AUTHOR | = | {Geleji, J{\'a}nos and Jord{\'a}n, Tibor}, |
| TITLE | = | {Robust tensegrity polygons}, |
| NOTE | = | {{\tt egres.elte.hu}}, |
| INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
| YEAR | = | {2012}, |
| NUMBER | = | {TR-2012-15} |