The (alpha =3, beta =2) member of the (A3ABO6) (A3B3O9) homologous series has been stabilised in the Sr-Rh-O system for a [Sr10(Sr0.5Rh1.5)TP(Rh6)Oh]O24 composition. The structural characterisation has been performed by powder X-ray and electron diffraction measurements and high-resolution electron microscopy. In this structure, three face-sharing [RhO6] octahedra linked by one [Rh/SrO6] trigonal prism comprise the infinite one-dimensional chain that runs parallel to the c axis of a trigonal unit cell (Pc1), with parameters a=9.6411(1) and c=21.2440(4) A.