  Given a finite metric CW complex $X$ and an element $\alpha \in \pi_n(X)$,
what are the properties of a geometrically optimal representative of $\alpha$?
We study the optimal volume of $k\alpha$ as a function of $k$. Asymptotically,
this function, whose inverse, for reasons of tradition, we call the volume
distortion, turns out to be an invariant with respect to the rational homotopy
of $X$. We provide a number of examples and techniques for studying this
invariant, with a special focus on spaces with few rational homotopy groups.
Our main theorem characterizes those $X$ in which all non-torsion homotopy
classes are undistorted, that is, their distortion functions are linear.
