  We analyze the zero-energy sector of the trigonal zigzag nanodisk and corner
based on the Dirac theory of graphene. The zero-energy states are shown to be
indexed by the edge momentum and grouped according to the irreducible
representation of the trigonal symmetry group $C_{3v}$. Wave functions are
explicitly constructed as holomorphic or antiholomorphic functions around the K
or K' point. Each zero-energy mode is a chiral edge mode. We find a texture of
magnetic vortices. It is intriguing that a vortex with the winding number $2$
emerges in the state belonging to the $E$ (doublet) representation. The
realization of such a vortex is vary rare.
