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Maximum quantity of enantiomorphs for a given form [closed]

-1

$begingroup$

Are there forms or spaces permitting a given chiral form to have more than one enantiomorph?

geometry terminology knot-theory

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asked Apr 2 at 15:27

bblohowiakbblohowiak

6310

$endgroup$

closed as off-topic by Shailesh, José Carlos Santos, N. Owad, Kyle Miller, Eevee Trainer Apr 16 at 3:28

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Shailesh, José Carlos Santos, Eevee Trainer

If this question can be reworded to fit the rules in the help center, please edit the question.

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  What is an enantiomorph? You need to give a lot more background here to get an answer I think.
  $endgroup$
  – N. Owad
  Apr 3 at 6:24
  

  
  
  
  


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  @N.Owad My understanding is that an asymmetric form in a given space may be able to have a "mirror image" that the form cannot be mapped to via rotation and translation; while this suggests that chiral forms may come in pairs, I would like to verify.
  $endgroup$
  – bblohowiak
  Apr 3 at 19:24
  

  
  
  
  


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  Maybe this question is about the (unoriented) mapping class group of the space acting on isotopy classes of knots? For example, the mapping class group of $S^3$ is $mathbbZ/2mathbbZ$, so there is a maximum of two distinct enantiomorphs of a knot. The double of a genus-$3$ handlebody seems to have knots that have (at least) three enantiomorphs. In any case, this question ought to be expanded and clarified.
  $endgroup$
  – Kyle Miller
  Apr 5 at 18:28
  

  
  
  
  


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  @KyleMiller Thank you for providing examples in your comment. Knot theory is certainly relevant to the question though desired responses need not be exclusive to that discipline. The example you offered of the double of a genus-3 handlebody having at least three enantiomorphs seems like it would qualify as an answer in the affirmative to the general question.
  $endgroup$
  – bblohowiak
  Apr 5 at 20:45
  

  
  
  
  

add a comment | 

-1

$begingroup$

Are there forms or spaces permitting a given chiral form to have more than one enantiomorph?

geometry terminology knot-theory

share|cite|improve this question

asked Apr 2 at 15:27

bblohowiakbblohowiak

6310

$endgroup$

closed as off-topic by Shailesh, José Carlos Santos, N. Owad, Kyle Miller, Eevee Trainer Apr 16 at 3:28

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Shailesh, José Carlos Santos, Eevee Trainer

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What is an enantiomorph? You need to give a lot more background here to get an answer I think.
  $endgroup$
  – N. Owad
  Apr 3 at 6:24
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @N.Owad My understanding is that an asymmetric form in a given space may be able to have a "mirror image" that the form cannot be mapped to via rotation and translation; while this suggests that chiral forms may come in pairs, I would like to verify.
  $endgroup$
  – bblohowiak
  Apr 3 at 19:24
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Maybe this question is about the (unoriented) mapping class group of the space acting on isotopy classes of knots? For example, the mapping class group of $S^3$ is $mathbbZ/2mathbbZ$, so there is a maximum of two distinct enantiomorphs of a knot. The double of a genus-$3$ handlebody seems to have knots that have (at least) three enantiomorphs. In any case, this question ought to be expanded and clarified.
  $endgroup$
  – Kyle Miller
  Apr 5 at 18:28
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @KyleMiller Thank you for providing examples in your comment. Knot theory is certainly relevant to the question though desired responses need not be exclusive to that discipline. The example you offered of the double of a genus-3 handlebody having at least three enantiomorphs seems like it would qualify as an answer in the affirmative to the general question.
  $endgroup$
  – bblohowiak
  Apr 5 at 20:45
  

  
  
  
  

add a comment | 

$begingroup$

Are there forms or spaces permitting a given chiral form to have more than one enantiomorph?

geometry terminology knot-theory

share|cite|improve this question

asked Apr 2 at 15:27

bblohowiakbblohowiak

6310

$endgroup$

share|cite|improve this question

asked Apr 2 at 15:27

bblohowiakbblohowiak

6310

share|cite|improve this question

asked Apr 2 at 15:27

bblohowiakbblohowiak

6310

asked Apr 2 at 15:27

bblohowiakbblohowiak

6310

asked Apr 2 at 15:27

bblohowiakbblohowiak

6310