Understanding the schoenflies notation

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In summary, a hexagonal crystal can be described by a 6-fold rotation group, which refers to the set of 6-fold rotations that leave the crystal unchanged. The number of members in this group varies for 2D and 3D hexagonal lattices. Symmetry operations, such as reflections, can also be combined with the rotation group. For example, C6h includes a horizontal reflection plane in addition to the 6-fold rotations. The position of this plane is determined by its perpendicularity to the rotation axis.
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So let's take a hexagonal crystal. The term:
C6 then refers to the 6-fold rotation group. I litterarily have no idea about what a group is but still want to understand the basic things qualitatively.
So what is meant by the 6-fold rotation group? Is it the set of 6 fold rotations leaving the crystal invariant. How many members are there in the case of the 2d and 3d hexagonal lattice?
Combination of symmetry operations are also considered. For example:
C6h is the 6 fold rotation group plus the addition of a horizontal reflection plane. In this case, what specifies the position of this plane other than it being perpendicular to the rotation axis?
 
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1. What is the Schoenflies notation and how is it used?

The Schoenflies notation is a system of symbols and letters used to represent the symmetry elements of a molecule or crystal. It is often used in crystallography and chemistry to describe the symmetry of a structure. The notation is based on the work of German mathematician Arthur Schoenflies, who developed the system in the late 19th century.

2. How is the Schoenflies notation different from other symmetry notations?

The Schoenflies notation is different from other symmetry notations because it uses a combination of letters and numbers to represent the different symmetry elements. It also includes subscripts and primes to indicate the number of times a particular symmetry element is present. Other notations, such as the Hermann-Mauguin notation, use numbers and symbols to represent symmetry elements.

3. What are the different types of symmetry elements represented in the Schoenflies notation?

The Schoenflies notation includes the following symmetry elements: identity (E), rotations (Cn), improper rotations (Sn), reflections (σ), inversion (i), and rotoinversions (S2n). These elements can be combined to describe the overall symmetry of a molecule or crystal.

4. How is the Schoenflies notation used to describe the symmetry of molecules or crystals?

The Schoenflies notation is used to describe the symmetry of a molecule or crystal by assigning a set of symmetry elements to the structure. These elements are then combined using group theory to determine the overall point group symmetry of the molecule or crystal. This information can be used to predict physical properties and behavior of the structure.

5. How is the Schoenflies notation helpful in scientific research?

The Schoenflies notation is helpful in scientific research because it provides a standardized system for describing the symmetry of molecules and crystals. This allows scientists to communicate and compare their findings more effectively. Additionally, understanding the symmetry of a structure can provide valuable insights into its physical and chemical properties, which can aid in the development of new materials and drugs.

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