The directionality of the static friction force experienced by an atomically sharp tip driven by an elastic spring on a surface lattice with hexagonal symmetry is studied analytically. Provided that the interaction between tip and surface is sufficiently high, static friction is almost independent of the pulling direction. This behavior is quite different from kinetic friction, which is peaked along the main crystallographic directions of the surface lattice. This result is important for modeling mechanical properties of nanodevices based on graphene and manipulation on the nanometer scale.