4 problems

Whiteley's upper-bound conjecture. The number of members satisfies

Let $P$ be any “polytope” with a full-dimensional affine span in $\mathbb R^d$. Let $\mathbf p_{n+1}$ be placed anywhere in $\mathbb R^d$. Let $\Omega$ be any stress for the bar fr…

Let $P$ be a convex polytope with $n$ vertices and full-dimensional span in $\mathbb R^d$. Let $(G^*,\hat{\bf p})$ be the tensegrity framework on $n+1$ vertices obtained by putting…

Symmetric tensegrity analogue of Connelly's theorem. If $(\hat{G},p)$ has a cable or strut and no symmetry-preserving finite flex, then it has a fully symmetric, non-zero, proper s…