Given a graph $G=(V,E)$ and a length function $\ell:E\to\mathbb{R}_+$.
An embedding of the graph into the $d$-dimensional Euclidean space is a map $f:V\to\mathbb{R}^d$ such that $||f(u)-f(v)||=\ell(uv)$ if $uv\in E$. (So $(G,f)$ is actually a framework in terms of rigidity theory.)

I'm thinking about finding an embedding that maximize the volume of the convex hull of the points $f(v)$, $v\in V$ in $\mathbb{R}^d$ (the dimension in question is fixed).