  We construct convex bodies that can be "captured by nets." More precisely,
for each dimension $n \geq 2$, we construct a family of Riemannian $n$-spheres,
each with a stable geodesic net, which is a stable 1-dimensional integral
varifold. Small perturbations of a stable geodesic net must lengthen it. These
stable geodesic nets are composed of multiple geodesic loops based at the same
point, and also do not contain any closed geodesic. All of these Riemannian
$n$-spheres are isometric to convex hypersurfaces of $\mathbb{R}^{n+1}$ with
positive sectional curvature.
