We study the structural, electronic, and optical properties of the Pt-based vacancy-ordered double perovskites A(2)PtX(6) (A = K, Rb, Cs; X = Cl, Br, I) in the tetragonal P4/mnc polymorph using the relativistic all-electron calculations based on the density functional theory. It is found that the rotation angles. of the PtX6 octahedra are non-zero for all the compounds. For a given A-site cation,. increases from Cl to Br to I while for a given halide anion,. decreases from K to Rb to Cs. As a result, the largest. is found for K2PtI6. Taking the three iodides, K2PtI6, Rb2PtI6 and Cs2PtI6, as representatives, it is found that K2PtI6 is a direct-band-gap semiconductor and that Rb2PtI6 and Cs2PtI6 are quasi-direct-band-gap semiconductors with the small differences between the indirect and direct band gaps. The band gap in the tetragonal P4/mnc polymorph is larger than the corresponding one in the cubic Fm3m polymorph. Employing the spectroscopically limited maximum efficiency as a metric for quantifying the photovoltaic performance, K2PtI6, Rb2PtI6, and Cs2PtI6 are found to be promising absorber materials for thin-film solar cells.