One of the most interesting characteristics of crystals is their profound morphology. Polyhedron or polygon shapes are often observed in single crystals. The hierarchical structure and morphology of polymer crystals can be described at unit cell, single crystal and spherulite length scales. This article discusses the role of translational symmetry in the evolution of polymer crystal morphology from unit cell to single crystal level. We divide single crystal level crystalline structure into two categories: shape-translational symmetry commensurate crystals (SSCs) and shape-translational symmetry incommensurate crystals (SSICs). The former case includes classical lamellae, dendritic single crystals and epitaxy-driven crystal morphologies. In SSICs, we emphasize crystals’ non-flat shapes, which are incommensurate with translational symmetry in Euclidean space. Classical helicoidal, tubular and scrolled crystals are discussed in the context of SSICs. We further highlight the recently discovered spherical crystalsomes which are formed via miniemulsion solution crystallization. This article provides an overview of polymer crystal morphology based on the interplay between crystal shape and translational symmetry, which may be used to study and design morphologies of semicrystalline polymers and copolymers.

晶体最有趣的特征之一就是其深厚的形态。通常在单晶中观察到多面体或多边形形状。可以在晶胞，单晶和球晶的长度尺度上描述聚合物晶体的分层结构和形态。本文讨论了平移对称性在聚合物晶体形态从晶胞到单晶水平演变中的作用。我们将单晶级晶体结构分为两类：形状平移对称的适度晶体（SSC）和形状平移对称的适度晶体（SSIC）。前者包括经典薄片，树状单晶和外延驱动的晶体形态。在SSIC中，我们强调晶体的非平坦形状，与欧几里得空间中的平移对称性不相称。在SSIC中讨论了经典的螺旋，管状和滚动晶体。我们进一步强调了最近发现的通过细乳液溶液结晶形成的球形晶体。本文基于晶体形状和平移对称性之间的相互作用提供了聚合物晶体形态的概述，可用于研究和设计半结晶聚合物和共聚物的形态。