The electromagnetic properties of the SU(3)-flavor baryon decuplet are examined within a lattice simulation of quenched QCD. Electric charge radii, magnetic moments, and magnetic radii are extracted from the E0 and M1 form factors. Preliminary results for the E2 and M3 moments are presented, giving the first model-independent insight to the shape of the quark distribution in the baryon ground state. As in our octet-baryon analysis, the lattice results give evidence of spin-dependent forces and mass effects in the electromagnetic properties. The quark charge distribution radii indicate these effects act in opposing directions. Some baryon dependence of the effective quark magnetic moments is seen. However, this dependence in decuplet baryons is more subtle than that for octet baryons. Of particular interest are the lattice predictions for the magnetic moments of Ω- and Δ++ for which new recent experimental measurements are available. The lattice prediction of the Δ++p ratio appears larger than the experimental ratio, while the lattice prediction for the Ω-p magnetic moment ratio is in good agreement with the experimental ratio.