Affine Stresses, Inverse Systems, and Reconstruction Problems
Affine Stresses, Inverse Systems, and Reconstruction Problems
Abstract A conjecture of Kalai asserts that for $d\geq 4$, the affine type of a prime simplicial $d$-polytope $P$ can be reconstructed from the space of affine $2$-stresses of $P$. We prove this conjecture for all $d\geq 5$. We also prove the following generalization: for all pairs $(i,d)$ with $2\leq …