What is the relationship between C1h and C1v point groups in crystallography?

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In summary, cristallographic groups, also known as space groups, are mathematical groups that describe the symmetry of a crystal lattice. There are 230 unique groups, which can be further classified into 7 crystal systems. The symmetry of a crystal lattice, described by its cristallographic group, can greatly influence its physical and chemical properties. These groups are determined experimentally by analyzing the diffraction pattern of X-rays or electrons passing through a crystal. They have a wide range of applications in various fields, including materials science, mineralogy, chemistry, and biology.
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chikou24i
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How to draw the symettry axis for 1-fold rotation ? And why C1v is identical to C1h ?
Thanks
 
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Think about what a 1-fold rotation means!
 
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Oh ! I think 1-fold rotation means no symmetry so there is no axis of semmetry. Is that correct ?
 
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Mod note: This post was moved from a different thread.
Why the point group C1h is identical to C1v ?
Why the point group C1h with horizontal twofold axis is identical to C2v ?
Thanks
 
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1. What are cristallographic groups?

Cristallographic groups, also known as space groups, are mathematical groups that describe the symmetry of a crystal lattice. They are an essential tool for understanding the physical and chemical properties of crystals.

2. How many cristallographic groups are there?

There are 230 unique cristallographic groups, which can be further classified into 7 crystal systems based on their symmetry and unit cell shape. These systems include cubic, tetragonal, orthorhombic, hexagonal, monoclinic, triclinic, and trigonal.

3. How do cristallographic groups affect crystal properties?

The symmetry of a crystal lattice, described by its cristallographic group, can greatly influence its physical and chemical properties. For example, symmetry can determine the shape and cleavage of a crystal, as well as its optical, thermal, and electrical properties.

4. How are cristallographic groups determined?

Cristallographic groups are determined experimentally by analyzing the diffraction pattern of X-rays or electrons passing through a crystal. This information is used to determine the symmetry elements and operations present in the crystal lattice, which are then used to identify the appropriate cristallographic group.

5. What are some applications of cristallographic groups?

Cristallographic groups have a wide range of applications in various fields, including materials science, mineralogy, chemistry, and biology. They are used to study the structure and properties of crystals, design new materials with desired properties, and understand the behavior of molecules and proteins in a crystal lattice.

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