Calabi-Yau threefolds with small Hodge numbers

We present a master list of Calabi-Yau threefolds, known to us, with small Hodge numbers, which we understand to be those manifolds with height $(h^{1,1}+h^{2,1})\le 24$. With the completion of a project to compute the Hodge numbers of all free quotients of complete intersection Calabi-Yau threefolds by Candelas et. al. in [1-3], many new points have been added to the tip of the Hodge plot, updating the reviews by Davies and Candelas in [1,4]. In view of this and other recent constructions of Calabi-Yau threefolds with small height we have produced an updated list