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We study networks in $\R^n$ which are periodic under a lattice of rank~$n$and have vertices of prescribed degree $d\ge 3$. We minimize the length of thequotient networks, subject to the constraint that the fundamental domain has$n$-dimensional volume~$1$. For $n=3$ and degree $3\leq d\leq 6$ we determinethe minimizing networks with the least number of vertices in the quotient,while for $d\ge 7$ we state a length estimate. For general $n$, we determinethe unique minimizers with $d=n+1$ and $d=2n$.

Periodic networks of fixed degree minimizing length