  This Letter investigates the emergence of corner modes in elastic twisted
Kagome lattices at a critical twist angle, known as self-dual point. We show
that a special type of corner modes exist and they are localized at a very
specific type of corners independent of the overall shape of the finite
lattice. Moreover, these modes appear even in the perturbed lattice at the
corners with mirror planes. By exploring its counterpart in electronic system,
we attribute such corner modes to charge accumulation at the boundary, which is
confirmed by the plot of charge distribution in a finite lattice.
