2 problems

Let $S$ be a closed piecewise-linear surface, and let $(G_S^\star,\boldsymbol p)$ be its coned framework: the framework has the vertices and edges of $S$, together with a cone vert…

Let $S$ be a closed piecewise-linear surface, with facets indexed by $i$, unit facet normals $n_i$, facet volumes $V_i$, and dihedral angles $\theta_{FG}:=\angle(n_F,n_G)$. Conside…