The interaction energy of three adsorbates on a surface consists of the sum of the three-pair interactions plus a trio contribution produced primarily by interference of electrons which traverse the entire perimeter, d(123), of the three-adsorbate cluster. Here, we investigate this three-adatom interaction when mediated by the isotropic Shockley surface-state band found on noble-metal (111) surfaces, extending work on pair interactions. Our experimentally testable depends on the s-wave phase-shift, characterizing the standing-wave patterns seen in scanning-tunnelling microscopy (STM) images. Compared with the adsorbate-pair interactions, and in contrast to bulk-mediated interactions, the trio contribution exhibits a slightly weaker amplitude and a slightly faster asymptotic envelope decay, d(123)(-5/2). It also has a different but well-defined oscillation period dependent on d(123) and little dependence on the shape of the cluster. We finally compare the asymptotic description with exact model calculations assuming short-range interactions, which are viable even in the non-asymptotic range (when not outweighted by bulk-mediated interations). (C) 2003 Elservier Science B.V. All rights reserved.