  Any gentle algebra $A$ with one maximal path corresponds to a unique
quasi-diagram $\alpha$. We introduce the regularity for $\alpha$, and show that
$A$ has finite global dimension if and only if $\alpha$ is regular. We
characterize regular quasi-diagrams which remain regular under the dihedral
group action. We prove that the set of maximal chord diagrams is the "biggest"
one among the sets closed under taking Koszul dual and rotations.
