  For all integers $m \geq n \geq 2$, we exhibit infinite families of purely
periodic Jacobi-Perron Algorithm (JPA) expansions of dimension $n$ with period
length equal to $m$ along with the associated Hasse-Bernstein units. Some
observations on the units of Levesque-Rhin as well as the periodicity of the
JPA expansion of $\left( m^{1/3}, m^{2/3} \right)$ are also made.
