Euclidean simplices and invariants of three-manifolds: a modification of   the invariant for lens spaces
  We propose a modification of the three-manifold invariant based on the use of Euclidean metric values ascribed to the elements of manifold triangulation. We thus obtain a nontrivial invariant that can, in particular, distinguish non-homeomorphic lens spaces. 
Evgeniy V. Martyushev