Recent studies show that calix[4]arene‐based micelles are monodisperse with defined N_agg values chosen from 4, 6, 8, 12, 20, and 32. Interestingly, all these numbers coincide with the face numbers of Platonic solids, so they are called “Platonic micelles.” As long as a certain geometric condition is fulfilled, any amphiphilic molecule can form a Platonic micelle. The preferred N_agg values are explained in relation to the mathematical Tammes problem, namely, how to obtain the best coverage of a sphere's surface with multiple identical circles. The coverage ratio can be calculated and produces maxima at 4, 6, 12, 20, and 32, coinciding with the observed N_agg values. In this feature article, Platonic micelles as well as their morphological transition by controlling pH, salt, temperature, and electrostatic interactions are summarized.

中文翻译：

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具有与柏拉图固体相关的聚集数的单分散胶束。

最近的研究表明，基于杯[4]芳烃的胶束是单分散的，具有从_{4、6、8、12、20}和32中定义的N _agg值。有趣的是，所有这些数字与柏拉图固体的面数一致，因此它们被称为“柏拉图胶束”。只要满足一定的几何条件，任何两亲分子都可以形成柏拉图胶束。相对于数学Tammes问题（即如何获得具有多个相同圆的球体表面的最佳覆盖率）来解释首选的N _agg值。可以计算覆盖率并在4,6,12,20和32处产生最大值，与观察到的N _agg一致价值观。在这篇专题文章中，总结了柏拉图胶束及其通过控制pH，盐，温度和静电相互作用的形态转变。