  Hyperideal tetrahedra are the fundamental building blocks of hyperbolic
3-manifolds with geodesic boundary. The study of their geometric properties (in
particular, of their volume) has applications also in other areas of
low-dimensional topology, like the computation of quantum invariants of
3-manifolds and the use of variational methods in the study of circle packings
on surfaces.
  The Schl\"afli formula neatly describes the behaviour of the volume of
hyperideal tetrahedra with respect to dihedral angles, while the dependence of
volume on edge lengths is worse understood. In this paper we prove that, for
every $\ell<\ell_0$, where $\ell_0$ is an explicit constant, regular hyperideal
tetrahedra of edge length $\ell$ maximize the volume among hyperideal
tetrahedra whose edge lengths are all not smaller than $\ell$.
  This result provides a fundamental step in the computation of the ideal
simplicial volume of an infinite family of hyperbolic 3-manifolds with geodesic
boundary.
