  Geometrical spines are defined for 3-manifolds with natural metrics, in
particular, for lens manifolds. We show that any spine of L(p,q) close enough
to its geometrical spine (i.e., to the cut locus with respect to the standard
metric) contains at least E(p,q)-3 vertices, which is exactly the conjectured
value for Matveev's complexity of L(p,q); here E(p,q) stands for the sum of the
elements of the continued fraction expansion of p/q. As a byproduct, we find
the minimal (over all triangulations) rotation distance (the term coined by
Sleator, Tarjan, and Thurston) between a triangulation of a regular p-gon and
its image under (2Pi q/p)-rotation. This minimum is also equal to E(p,q)-3.
