Symmetry is an important component of geometric beauty and regularity in both natural and cultural scenes. Plants also display various geometric patterns with some kinds of symmetry, of which the most notable example is the arrangement of leaves around the stem, i.e., phyllotaxis. In phyllotaxis, reflection symmetry, rotation symmetry, translation symmetry, corkscrew symmetry, and/or glide reflection symmetry can be seen. These phyllotactic symmetries can be dealt with the group theory. In this review, we introduce classification of phyllotactic symmetries according to the group theory and enumerate all types of phyllotaxis, not only major ones such as spiral and decussate but also minor ones such as orixate and semi-decussate, with their symmetry groups. Next, based on the mathematical model studies of phyllotactic pattern formation, we discuss transitions between phyllotaxis types different in the symmetry class with a focus on the transition into one of the least symmetric phyllotaxis, orixate, as a representative of the symmetry-breaking process. By changes of parameters of the mathematical model, the phyllotactic pattern generated can suddenly switch its symmetry class, which is not constrained by the group-subgroup relationship of symmetry. The symmetry-breaking path to orixate phyllotaxis is also accompanied by dynamic changes of the symmetry class. The viewpoint of symmetry brings a better understanding of the variety of phyllotaxis and its transition.

在自然和文化场景中，对称都是几何美感和规律性的重要组成部分。植物还表现出具有某些对称性的各种几何图案，其中最著名的例子是茎周围的叶子排列，即叶序。在叶序中，可以看到反射对称，旋转对称，平移对称，开瓶器对称和/或滑行反射对称。这些系统叶对称性可以用群论来处理。在这篇综述中，我们根据群论介绍了叶序对称性的分类，并列举了所有类型的叶序，不仅是螺旋形和蝶形的主要种类，还有欧利酸盐和半蝶形的次要种类，以及它们的对称性种类。接下来，基于叶序模式形成的数学模型研究，我们讨论了对称类别中不同的叶轴类型之间的过渡，重点是过渡到最小对称的叶轴之一，orixate，作为对称性破坏过程的代表。通过更改数学模型的参数，生成的叶序模式可以突然切换其对称性类别，不受对称性的组-子组关系的约束。Orixate phyllotaxis的对称性破坏路径还伴随着对称性类别的动态变化。对称性观点使人们更好地了解了叶序的种类及其过渡。通过更改数学模型的参数，生成的叶序模式可以突然切换其对称性类别，不受对称性的组-子组关系的约束。Orixate phyllotaxis的对称性破坏路径还伴随着对称性类别的动态变化。对称性观点使人们更好地了解了叶序的种类及其过渡。通过更改数学模型的参数，生成的叶序模式可以突然切换其对称性类别，不受对称性的组-子组关系的约束。Orixate phyllotaxis的对称性破坏路径还伴随着对称性类别的动态变化。对称性观点使人们更好地了解了叶序的种类及其过渡。