Sr_3(Ru_{0.336},Pt_{0.664})CuO_6 crystallizes as a monoclinic structure [space group R12/c; lattice parameters a = 9.595 (15), b = 9.595 (15), c = 11.193 (2) Å and \gamma = 120°]. The crystal structure is pseudotrigonal and the crystal investigated here by single-crystal X-ray diffraction was a multiple twin composed of six individuals. The twin laws are a combination of rhombohedral obverse/reverse twinning plus the threefold axis from the trigonal system. The crystal structure is related to the hexagonal perovskites. Each Pt/Ru atom is coordinated pseudo-octahedrally by O atoms, while the overall coordination polyhedra for Cu atoms can be regarded as a strongly distorted trigonal prism, where the Cu atom is clearly shifted from the center. Each [(Ru_{0.336},Pt_{0.664})O_6] octahedron is connected to two Cu—O polyhedra via a common edge, and thus chains are formed parallel to the crystallographic c axis. Sr^{2+} ions are incorporated between the chains and are coordinated by eight O atoms. All bond distances and angles are in good agreement with literature values. Electron-microscopy studies confirm the results from X-ray diffraction and all observed domain structures can be interpreted exactly with the established twin model. No indication of Pt/Ru ordering was found in either the X-ray or the electron-microscopy investigation.