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

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How to draw the symettry axis for 1-fold rotation ? And why C1v is identical to C1h ?
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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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