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Inspired by the recent progress by Coates-Corti-Kasprzyk et al. on MirrorSymmetry for del Pezzo surfaces, we show that for any positive integer k thedeformation families of del Pezzo surfaces with a single 1/k(1,1) singularity(and no other singular points) fit into a single cascade. Additionally weconstruct models and toric degenerations of these surfaces embedded in toricvarieties in codimension less than or equal two. Several of these directlygeneralise constructions of Reid-Suzuki (in the case k=3). We identify a rootsystem in the Picard lattice, and in light of the work of Gross-Hacking-Keel,comment on Mirror Symmetry for each of these surfaces. Finally we classify alldel Pezzo surfaces with certain combinations of 1/k(1,1) singularities fork=3,5,6 which admit a toric degeneration.

Del Pezzo surfaces with a single 1/k(1,1) singularity