Coverings and Minimal Triangulations of 3-Manifolds

This paper uses results on the classification of minimal triangulations of 3-manifolds to produce additional results, using covering spaces. Using previous work on minimal triangulations of lens spaces, it is shown that the lens space $L(4k,2k-1)$ and the generalised quaternionic space $S^3\mathrm{/}{Q}_{4k}$ have complexity $k,$ where $k\ge 2.$ Moreover, it is shown that their minimal triangulations are unique.