  The two-sided BTZ black hole has been instrumental in elucidating several
aspects of AdS/CFT. Similarly, multiboundary wormholes provide a useful and
rich arena in which probing questions of quantum gravity can be posed and
explored. In this work, we find the explicit forms of the Killing vectors
needed to construct three-boundary wormholes, with and without rotation, as
quotients of AdS$_3$. We ensure that our method captures the full moduli space
of such wormholes and elaborate on the generalization of our procedure to more
exotic multiboundary spaces, including higher genus.
