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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 aconsequence, Shafarevich's conjecture holds true for these families. Moreover,it follows from Deligne-Mostow and Mostow that, for $n=3$, it can be partiallycompactified 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 anarithmetic ball quotient.

Maximal families of Calabi-Yau manifolds with minimal length Yukawa coupling