When you look in the mirror, you form a symmetrical relationship with the image in the mirror. Symmetry appears not only in the mirror, but also in the nature around us. Honeycomb is a building that is symmetrically arranged by regular hexagons. Each regular hexagon is even in size and the distance from top to bottom is equal. This structure is the most compact and orderly, and it also saves the most materials. The structure of the butterfly's left and right wings is symmetrical, even the patterns and colors on the wings are symmetrical, so it can become the most beautiful insect in nature; All conchs have wonderful left-right rotational symmetry; People themselves are symmetrical, not only the left and right structures are symmetrical, but also the shapes of eyes, ears and left and right brains. Imagine that a person who is missing an eye or has a crooked mouth will definitely be considered not very beautiful.

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.