  For each natural odd number $n\geq 3$, we exhibit a maximal family of
$n$-dimensional Calabi-Yau manifolds whose Yukawa coupling length is one. As a
consequence, Shafarevich's conjecture holds true for these families. Moreover,
it follows from Deligne-Mostow and Mostow that, for $n=3$, it can be partially
compactified to a Shimura family of ball type, and for $n=5,9$, there is a sub
$\mathbb Q$-PVHS of the family uniformizing a Zariski open subset of an
arithmetic ball quotient.
