  Let $P$ be a convex polyhedron in $\mathbb{R}^3$. The skeleton of $P$ is the
graph whose vertices and edges are the vertices and edges of $P$, respectively.
We prove that, if these vertices are on the unit-sphere, the skeleton is a
$(0.999 \cdot \pi)$-spanner. If the vertices are very close to this sphere,
then the skeleton is not necessarily a spanner. For the case when the boundary
of $P$ is between two concentric spheres of radii $1$ and $R>1$, and the angles
in all faces are at least $\theta$, we prove that the skeleton is a
$t$-spanner, where $t$ depends only on $R$ and $\theta$. One of the ingredients
in the proof is a tight upper bound on the geometric dilation of a convex cycle
that is contained in an annulus.
