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Let $P$ be a convex polyhedron in $\mathbb{R}^3$. The skeleton of $P$ is thegraph 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 boundaryof $P$ is between two concentric spheres of radii $1$ and $R>1$, and the anglesin 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 ingredientsin the proof is a tight upper bound on the geometric dilation of a convex cyclethat is contained in an annulus.

On the Stretch Factor of Convex Polyhedra whose Vertices are (Almost) on a Sphere