Understanding the schoenflies notation

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Discussion Overview

The discussion centers on the Schoenflies notation, particularly in relation to hexagonal crystals and their symmetry operations. Participants explore the meaning of the 6-fold rotation group and its implications in both 2D and 3D hexagonal lattices, as well as the addition of reflection planes in this context.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses uncertainty about the concept of a group and seeks a qualitative understanding of the 6-fold rotation group, questioning whether it refers to the set of rotations that leave the crystal invariant.
  • The same participant inquires about the number of members in the 6-fold rotation group for both 2D and 3D hexagonal lattices.
  • The participant also mentions that combinations of symmetry operations are considered, specifically referencing C6h, which includes a horizontal reflection plane, and asks what specifies the position of this plane aside from its perpendicularity to the rotation axis.

Areas of Agreement / Disagreement

The discussion does not appear to reach a consensus, as participants are exploring foundational concepts and raising questions without definitive answers or agreement on the interpretations of the notation.

Contextual Notes

Participants have not established definitions for key terms such as "group" or "symmetry operations," and there are unresolved questions regarding the specifics of the 6-fold rotation group and the implications of reflection planes.

aaaa202
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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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