2022/12/26 by Fatemeh Mohammadi, Xian Wu, Mohammadi, Fatemeh +1
Computer Science · #Advanced Graph Theory Research #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2212.13189
openalex publication_date 2022/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 F, we construct a glued toric surface XF. We show that the abelian group of tensegrities on F is isomorphic to a subgroup of the Chow group A1(XF;\QQ). In the case of planar frameworks, we show how to explicitly carry out the computation of tensegrities via classical tools in toric geometry.