Scientific observation has led to the discovery of recurring patterns in nature. Symmetry is the property of an object showing regularity in parts on a plane or around an axis. There are several types of symmetries observed in the natural world and the most common are mirror symmetry, radial symmetry, and translational symmetry. Symmetries can be continuous or discrete. A discrete symmetry is a symmetry that describes non-continuous changes in an object. A continuous symmetry is a repetition of an object an infinite number of times. A consequence of continuous symmetry is the existence of conservation laws. A natural system with discrete and continuous symmetries displays several physical properties, such as the existence of long-range order. Geometric shapes exhibit symmetry as mirror reflections of each other. Symmetry in nature has been a model of beauty since the beginning of civilization. Since the earliest times, nature itself has manifestly been a model, evincing regularity in sundry forms and occurrences–from minerals and plants to the anatomy of living beings, to the regularly recurring stellar constellations. For Ancient Greek philosophers, proportion, symmetry, and harmony, were the basics to determine whether something is beautiful or not. Ancient Greek philosophers were known for bringing logic and rational thinking to phenomena that were previously explained by mythology and Gods. They observed the natural world around them and used their knowledge to answer questions about the proportion in observable objects and the origin of Earth. The Greek words summetria and summetros appear frequently in the Timaeus, defined as parts with each other and with the whole. Plato has a very rough concept of symmetry, and when he uses “beauty” to characterize the so-called Platonic Solids in the Timaeus, he seems to be emphasizing their regularity and indirectly their symmetry. Plato believes the four elements (earth, air, fire, water) have been constructed by the Demiurge, or a divine craftsman who appoints order in an otherwise chaotic universe. Minerals are representative examples of beauty, order, and symmetry in inorganic materials. Well-formed minerals (crystals) are a collection of equivalent faces related by symmetry. The goal of this paper is to relate the perspective of symmetry in ancient Greek philosophy with the modern scientific evidence of the geometric description of crystal structures. The five Platonic solids are ideal models of geometrical patterns that occur throughout the world of minerals. In this paper, minerals serve as a model of connecting the symmetry theory in Plato’s philosophy and modern advances in mineralogy.

科学观察导致发现了自然界中反复出现的模式。对称性是物体在平面上或围绕轴的部分显示出规律性的属性。在自然界中观察到的对称有几种类型，最常见的是镜像对称、径向对称和平移对称。对称可以是连续的或离散的。离散对称是描述对象中非连续变化的对称。连续对称是一个对象无限次地重复。连续对称的一个结果是存在守恒定律。具有离散和连续对称性的自然系统显示出多种物理特性，例如存在长程有序。几何形状表现出对称性，就像彼此的镜面反射一样。自文明开始以来，自然界的对称性一直是美的典范。从最早的时代开始，自然本身显然就是一个模型，以各种形式和事件表现出规律性——从矿物和植物到生物的解剖结构，再到定期出现的恒星星座。对于古希腊哲学家来说，比例、对称和和谐是决定事物美与否的基础。古希腊哲学家以将逻辑和理性思维带入以前由神话和众神解释的现象而闻名。他们观察周围的自然世界，并利用他们的知识回答有关可观察物体的比例和地球起源的问题。希腊词 自然本身显然是一个模型，以各种形式和事件表现出规律性——从矿物和植物到生物的解剖结构，再到定期出现的恒星星座。对于古希腊哲学家来说，比例、对称和和谐是决定事物美与否的基础。古希腊哲学家以将逻辑和理性思维带入以前由神话和众神解释的现象而闻名。他们观察周围的自然世界，并利用他们的知识回答有关可观察物体的比例和地球起源的问题。希腊词 自然本身显然是一个模型，以各种形式和事件表现出规律性——从矿物和植物到生物的解剖结构，再到定期出现的恒星星座。对于古希腊哲学家来说，比例、对称和和谐是决定事物美与否的基础。古希腊哲学家以将逻辑和理性思维带入以前由神话和众神解释的现象而闻名。他们观察周围的自然世界，并利用他们的知识回答有关可观察物体的比例和地球起源的问题。希腊词 对于古希腊哲学家来说，比例、对称和和谐是决定事物美与否的基础。古希腊哲学家以将逻辑和理性思维带入以前由神话和众神解释的现象而闻名。他们观察周围的自然世界，并利用他们的知识回答有关可观察物体的比例和地球起源的问题。希腊词 对于古希腊哲学家来说，比例、对称和和谐是决定事物美与否的基础。古希腊哲学家以将逻辑和理性思维带入以前由神话和众神解释的现象而闻名。他们观察周围的自然世界，并利用他们的知识回答有关可观察物体的比例和地球起源的问题。希腊词 他们观察周围的自然世界，并利用他们的知识回答有关可观察物体的比例和地球起源的问题。希腊词 他们观察周围的自然世界，并利用他们的知识回答有关可观察物体的比例和地球起源的问题。希腊词夏季和夏季经常出现在 Timaeu​​s 中，被定义为相互之间和整体的部分。柏拉图对对称的概念非常粗略，当他用“美”来形容蒂迈欧中所谓的柏拉图立体时，他似乎是在强调它们的规律性，而间接地强调它们的对称性。柏拉图相信四大元素（土、气、火、水）是由造物主（Demiurge）或一位神工匠建造的，他在原本混乱的宇宙中指定了秩序。矿物质是无机材料中美丽、有序和对称性的代表性例子。结构良好的矿物（晶体）是由对称相关的等效面的集合。本文的目的是将古希腊哲学中的对称性观点与晶体结构几何描述的现代科学证据联系起来。五种柏拉图立体是遍及矿物世界的几何图案的理想模型。在本文中，矿物作为连接柏拉图哲学中的对称理论与现代矿物学进展的模型。