  A classical tensegrity model consists of an embedded graph in a vector space
with rigid bars representing edges, and an assignment of a stress to every edge
such that at every vertex of the graph the stresses sum up to zero. The
tensegrity frameworks have been recently extended from the two dimensional
graph case to the multidimensional setting. We study the multidimensional
tensegrities using tools from toric geometry. For a given rational tensegrity
framework $\mathcal{F}$, we construct a glued toric surface $X_\mathcal{F}$. We
show that the abelian group of tensegrities on $\mathcal{F}$ is isomorphic to a
subgroup of the Chow group $A^1(X_\mathcal{F};\QQ)$. In the case of planar
frameworks, we show how to explicitly carry out the computation of tensegrities
via classical tools in toric geometry.

Algebraic Geometry;Combinatorics