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The notion of a layered triangulation of a lens space was defined by Jaco and Rubinstein, 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  n  ⩾ 2, the minimal layered triangulation of the lens space  L (2 n , 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 space of the form  L (2 n , 1).

Minimal triangulations for an infinite family of lens spaces