A motion that does not move or rotates 360 degrees is called an identity operation, and the corresponding symmetry element is called an identity element, denoted as E

The rotation operation is the operation of rotating the molecule around a certain axis to restore it, denoted as C

If there is a plane in the molecule that reflects the two halves of the molecule to each other and can restore the molecule, then the plane mirror is a mirror.

If you extend a straight line from any atom in the molecule to the center of symmetry, you will find another identical atom on the other side equidistant from the center of symmetry. The symmetry operation corresponding to the symmetry center is called inversion or inversion.

A collection of elements that are related to each other according to certain operating rules. The elements can be operations, matrices, operators, numbers, etc.

Closeness, main operation, inverse operation, associativity

If we know that the elements of a group are n and that all possible products are n2, then the group is completely and uniquely determined. n is the order of the group, that is, the number of equivalent parts in the object. List the products of group elements to get a multiplication table. Assume that the column element is A and the row element is B, then the product is AB, column x is row, row element B acts first, and column element A acts later.

When two symmetrical elements exist at the same time in a certain relative position, a third symmetrical element must be derived, which is called a combination of symmetrical elements. The combination of symmetrical elements obeys certain combination principles.

The product of two rotations must be another rotation

The combination of two mirrors is a rotation operation

The combination of an even axis of rotation and a mirror perpendicular to it

C1 group

This group

Cs group

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Dn group

Dnh group

Dnd group

Point group containing more than two higher-order axes Cn

Regular tetrahedron group: T, Td, Th

Cube or octahedron group

icosahedral group