Bravais Lattice in Two Dimensions

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Discussion Overview

The discussion revolves around the concept of Bravais lattices in two dimensions, specifically addressing the number of point groups in 2D and 3D, as well as the implications of these groups for the formation of Bravais lattices. Participants explore the definitions, examples, and reasoning behind the numbers presented in a physics textbook.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the number of point groups in three dimensions, suggesting there are 32 based on their understanding.
  • Another participant agrees with the assertion of 32 point groups in 3D and attempts to clarify the relationship between point groups and symmetry operations.
  • There is a request for a simpler explanation of how the 10 point groups in 2D lead to only 5 Bravais lattices, indicating a desire for pedagogical clarity.
  • A participant emphasizes the additional degrees of freedom in 3D that allow for more symmetry operations, which contributes to the higher number of point groups compared to 2D.
  • One participant expresses confusion about how the 10 point groups in 2D are derived and seeks examples to better understand the transition to 32 point groups in 3D.

Areas of Agreement / Disagreement

Participants generally agree on the number of point groups in 2D and 3D, but there is a lack of consensus on the explanation of how these groups are derived and their implications for Bravais lattices.

Contextual Notes

Participants express uncertainty regarding the derivation of the point groups and the relationship between point groups and Bravais lattices, indicating that further clarification and examples are needed.

shayaan_musta
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In the book Applied Physics by P.K.Mittal, on page#25 under the heading of "Bravais lattice in two dimensions", a paragraph says,
"The number of point groups in two dimensions is 10."
My 1st question is,
Then how many in three dimensions?

Paragraph further says,
"10 groups in two dimensions produce only 5 Bravais lattice."
What is meant by above statement?
 
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I believe there are 32 point groups in 3D.
 
Foder said:
I believe there are 32 point groups in 3D.

Thanks Foder.
Yes I agree with you. But in 2D there are 10 point groups then how will you justify this statement in a simple and easy language so that I could be able to teach other for their difficulties.
 
3D have more point groups than 2D because of the extra degree of freedom. I mean, point groups represent symmetry operations, such as inversions, reflections and rotations. When you add an extra dimension you can perform those in new directions not parallel to the original 2D plane, allowing also more combinations of them.
 
Yeah Foder I agree with you.
But I think you are not understanding my question.

Look, there are 10 point groups in 2D which are given below,
C1, C2, C3, C4, C6, D1, D2, D3, D4, D6

Agree?

Then I want to know that how these group can be created?

Means there was any genius who discovered that there are 10 point groups in 2D. So how he did it?
If you give one or two example then may be I would be able to understand that how there are 32 point groups in 3D.

I hope now you can understand my question.
Thanks for hard working for me. GOD bless you.
 

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