4 problems

Let a block and hole polyhedron $\mathcal{P}$ have cut cycles $\mathcal{C}$ of size $c$, and let $\mathcal{P}_{C}'$ denote each corresponding component, with block sizes $b_i'$ and…

Let an abstract block and hole polyhedron have graph symmetry group $\Phi(\mathcal{S})$, with no vertices or edges fixed. Symmetry-preserving contraction conjecture. There is a sym…

Let $S$ be a $4$-connected convex triangulated sphere, and remove one edge from its triangulation. Kuiper's conjecture. The resulting polyhedral framework should have a finite moti…

Let a block and hole polyhedron $\widehat{\mathcal{P}}$ satisfy the separation conditions: two blocks and two holes intersect in at most two vertices, intersections in two vertices…