Humans have advocated the beauty of symmetry since ancient times, and the concept of symmetry has penetrated into almost all disciplines. In architecture, architects are always inseparable from symmetry when planning, designing and building various buildings. Most famous buildings handed down from ancient times are extremely symmetrical, such as the Forbidden City in China, the Temple of Heaven, the promenade in the Summer Palace, the Great Pyramid in Egypt and the Colosseum in Rome. Geometrically, there are various symmetries such as circle, ellipse, square, rectangle, trapezoid, triangle, cone and cylinder. In algebra, there is a symmetry of two roots of a quadratic equation, a symmetric function of the equation, and even a mathematical theory of symmetric group theory.
In crystallography, symmetry is particularly prominent. In fact, there are few things in nature that are completely symmetrical with 100%, but crystals are an exception. No matter from the macroscopic or microscopic point of view, crystals are strictly symmetrical. There are many atoms in the crystal, and there is a strict spatial arrangement. If you draw a part of the atomic arrangement diagram at will, whether it is translation, rotation or left-right exchange, the obtained image can not be distinguished from the original image, that is to say, most crystals have the properties of translation symmetry, rotation symmetry and mirror symmetry. For example, the snowflake has a six-fold rotational symmetry, that is, after the snowflake crystal rotates 60 degrees, 120 degrees, 180 degrees, 240 degrees, 300 degrees or 360 degrees along a fixed axis, the spatial arrangement of its atoms is exactly the same as the original arrangement.