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

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SUMMARY

The discussion clarifies the relationship between the C1h and C1v point groups in crystallography, emphasizing that both groups exhibit identical symmetry properties. C1h features a horizontal mirror plane, while C1v includes vertical mirror planes, yet both represent systems with a single symmetry element, specifically a 1-fold rotation. The confusion regarding the definition of a 1-fold rotation is addressed, confirming that it implies the absence of symmetry axes.

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  • Understanding of crystallographic point groups
  • Familiarity with symmetry operations in three-dimensional space
  • Knowledge of mirror planes and rotational axes
  • Basic concepts of crystallography and molecular symmetry
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  • Study the implications of symmetry operations on molecular geometry
  • Explore the differences between horizontal and vertical mirror planes
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Students and professionals in crystallography, chemists studying molecular symmetry, and anyone interested in the mathematical foundations of symmetry in physical sciences.

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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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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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