Polycrystalline RERh6Si4 (RE=La, Nd, Tb, Dy, Er, Yb) samples can be synthesized by arc-melting of the elements. Single crystals of LaRh6Si4, NdRh6Si4 and YbRh6Si4 were synthesized from the elements in bismuth fluxes (non-reactive flux medium). The structures were refined on the basis of single-crystal X-ray diffractometer data: LiCo6P4 type, P6̅m2, a=700.56(3), c=380.55(1) pm, wR2=0.0257, 317 F2 values, 19 variables for LaRh6Si4, a=698.4(5), c=377.7(2) pm, wR2=0.0578, 219 F2 values, 19 variables for NdRh6Si4 and a=696.00(3), c=371.97(1) pm, wR2=0.0440, 309 F2 values, 19 variables for YbRh6Si4. The rhodium and silicon atoms build up three-dimensional, covalently bonded [Rh6Si4]δ− polyanionic networks with Rh–Si distances ranging from 239 to 249 pm. The rare earth atoms fill larger cavities within channels of these networks and they are coordinated by six silicon and twelve rhodium atoms in the form of hexa-capped hexagonal prisms.