Previous studies of the magnetic and structural properties of LaRh 6B 4 and CeRh 6B 4 have been extended to include the remaining members of the hexagonal ternary compound series RERh 6B 4 for REPr to Lu and Y. Across the entire series the rare earth (RE) component is found to be trivalent. To the accuracy of powder x-ray diffraction techniques, all compounds appear to be isostructural. YbRh 6B 4 orders magnetically at 140 mK and displays a Kondo-like resistivity anomaly. Contrary to earlier reports by other groups, LaRh 6B 4, EuRh 6B 4 and YRh 6B 4 do not order magnetically above ∼50 mK. None of the compounds in the series is superconducting above ∼50 mK.