Figure 1. Sketch of the different structures considered in this study.

(a) A hexagonally-ordered spherical cap of radius $R$ and geodesic radius ${\rho }_0$ without defects; (b) a spherical cap with a single disclination at the center (as shown) or multiple disclinations; (c) a rectangular ribbon with length $L$ and width $W$, that it is called belt when the length becomes $L=2\pi R$; and (d) a cylindrical patch with size $L$, that eventually becomes a cylinder of radius $R$. In the bending-dominated regime, $R=R_0$.