  We consider heteroclinic networks between $n \in \mathbb{N}$ nodes where the
only connections are those linking each node to its two subsequent neighbouring
ones. Using a construction method where all nodes are placed in a single
one-dimensional space and the connections lie in coordinate planes, we show
that it is possible to robustly realise these networks in $\mathbb{R}^6$ for
any number of nodes $n$ using a polynomial vector field. This bound on the
space dimension (while the number of nodes in the network goes to $\infty$) is
a novel phenomenon and a step towards more efficient realisation methods for
given connection structures in terms of the required number of space
dimensions. We briefly discuss some stability properties of the generated
heteroclinic objects.
