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We present a list of Calabi‐Yau threefolds known to us, and with holonomy groups that are precisely    S  U  (  3  )   , rather than a subgroup, with small Hodge numbers, which we understand to be those manifolds with height    (   h   1  ,  1    +   h   2  ,  1    )  ≤  24   . With the completion of a project to compute the Hodge numbers of free quotients of complete intersection Calabi‐Yau threefolds, most of which were computed in Refs. [[1][P. Candelas, 2010], [2][P. Candelas, 2012], [3][P. Candelas, 2015]] and the remainder in Ref. [[4][A. Constantin, 2017]], many new points have been added to the tip of the Hodge plot, updating the reviews by Davies and Candelas in Refs. [[1][P. Candelas, 2010], [5][R. Davies, 2011]]. In view of this and other recent constructions of Calabi‐Yau threefolds with small height, we have produced an updated list.

Calabi‐Yau Threefolds with Small Hodge Numbers