  The notion of a layered triangulation of a lens space was defined by Jaco and
Rubinstein in earlier work, and, unless the lens space is L(3,1), a layered
triangulation with the minimal number of tetrahedra was shown to be unique and
termed its "minimal layered triangulation." This paper proves that for each
integer n>1, the minimal layered triangulation of the lens space L(2n,1) is its
unique minimal triangulation. More generally, the minimal triangulations (and
hence the complexity) are determined for an infinite family of lens spaces
containing the lens spaces L(2n,1).
