Polymer single crystals consisting of folded chains are always in a nonequilibrium state, even if they are faceted with a well-defined envelope reflecting the parameters of the crystal unit cell. Heterogeneities like small variations in the degree of chain folding within such crystals are responsible for a rather broad range in melting temperature. Consequently, upon annealing at a given temperature, some parts may be above and some below their respective melting temperatures, inducing a lamellar thickening process, which may vary locally. To emphasize such variations, controlled annealing experiments are performed at comparatively low temperatures and for long times. For single crystals of low-molecular-weight polyethylene, the formation of the well-known "Swiss-cheese"-like morphology with randomly distributed holes of varying sizes within the annealed single crystal is observed. However, for high-molecular-weight polyethylene, a regular pattern appeared upon annealing, characterized by branches of equal width that are oriented perpendicular to the crystal edge. All branches end at the nucleation site. Interestingly, the resulting pattern depends sensitively on both crystallization and annealing conditions. These thermally induced regular patterns within a single crystal are attributed to a stable crystalline framework formed within polyethylene single crystals in the course of growth.