| Özet: | <p>We analyze freely-acting discrete symmetries of Calabi–Yau three-folds defined as hypersurfaces in ambient toric four-folds. An algorithm that allows the systematic classification of such symmetries which are linearly realised on the toric ambient space is devised. This algorithm is applied to all Calabi–Yau manifolds with <i>h</i><sup>1,1</sup>(<i>X</i>)≤3 obtained by triangulation from the Kreuzer–Skarke list, a list of some 350 manifolds. All previously known freely-acting symmetries on these manifolds are correctly reproduced and we find five manifolds with freely-acting symmetries. These include a single new example, a manifold with a ℤ<sub>2</sub>×ℤ<sub>2</sub> symmetry where only one of the ℤ<sub>2</sub> factors was previously known. In addition, a new freely-acting ℤ<sub>2</sub> symmetry is constructed for a manifold with <i>h</i><sup>1,1</sup>(<i>X</i>)=6. While our results show that there are more freely-acting symmetries within the Kreuzer–Skarke set than previously known, it appears that such symmetries are relatively rare.</p>
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