  We classify toric log del Pezzo surfaces of Picard number one by introducing
the notion, cascades. As an application, we show that if such a surface is
K\"ahler-Einstein, then it should admit a special cascade, and it satisfies the
equality of the orbifold Bogomolov-Miyaoka-Yau inequality, i.e., $K^2 =
3e_{orb}.$

Algebraic Geometry