  We extend the dictionary between Type IIB branes and representations of the
Ding-Iohara-Miki (DIM) algebra to the case when one of the space directions is
a circle. It is well-known that the worldvolume theory on branes wrapping the
circle is a 5d $\mathcal{N}=1$ gauge theory with adjoint matter, or more
generally of cyclic quiver type, and the corresponding intertwiners of the DIM
algebra give their Nekrasov partition functions. However, we find that there
exists a much wider natural class of intertwiners corresponding to branes
spiralling around the compactified direction, with many interesting properties.
We consider two examples, one corresponding to a spiralling D5 brane and
another to a D3 brane. The former gives rise to the K-theoretic vertex function
counting sheaves on $\mathbb{C}^3$ while the latter produces the
"non-stationary elliptic Ruijsenaars wavefunctions" introduced recently by
Shiraishi.
