Credit: Y. Wang/Penn State
(Left panel) Laying down square tiles starts off perfectly on the surface of a cone but ends up with an inevitable jagged border across which the two tiles orient incompatibly.
(Right panel) Similarly, a grain boundary forms when graphene growth advances past an apex on a conical bump, where the curvature resembles that on a sphere; it terminates at the foot of the bump, where curvature is saddle-like.