Infra-red multiple-photon dissociation spectroscopy on Xe-tagged Re/Si clusters, [ReSin]+, n = 3-9, reveals intense absorption features around 400 cm-1, along with, in some cases, additional bands in the 250-350 cm-1 window. A survey of the potential energy surface using density functional theory in conjunction with particle swarm optimisation indicates a growth pattern based on a growing network of Si atoms wrapped around the Re centre: the Sin units can be viewed as fragments of a putative 16-vertex Frank-Kasper polyhedron. The structural evolution for the [ReSin]+ series differs significantly from the iso-electronic Mn series studied previously, where the metal ion is typically bound externally to the surface of a growing 3-dimensional Sin cluster, the differences reflecting the greater accessibility of 5d vs. 3d electron density.