Understanding the schoenflies notation

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SUMMARY

The discussion focuses on the Schoenflies notation, specifically the C6 notation, which denotes the 6-fold rotation group associated with hexagonal crystals. The C6 group consists of six distinct rotational symmetries that leave the crystal invariant. Additionally, the C6h notation includes a horizontal reflection plane, which is defined as being perpendicular to the rotation axis. The conversation also touches on the combination of symmetry operations in both 2D and 3D hexagonal lattices.

PREREQUISITES
  • Understanding of symmetry operations in crystallography
  • Familiarity with hexagonal crystal structures
  • Knowledge of group theory concepts
  • Basic comprehension of Schoenflies notation
NEXT STEPS
  • Research the properties of the C6 rotation group in crystallography
  • Study the implications of horizontal reflection planes in symmetry operations
  • Explore the differences between 2D and 3D hexagonal lattices
  • Learn about other Schoenflies notations and their applications in crystallography
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Students and researchers in crystallography, materials science professionals, and anyone interested in the mathematical aspects of crystal symmetry and group theory.

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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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