Conformations of Cyclohexane

Is there any such thing as a twist chair conformation?


Also, the boat and the chair conformations are achiral, while the twist boat conformation of cyclohexane is chiral and dissymetric.
What about the half chair conformation? Am I right in thinking that it is achiral because it has a plane of symmetry?




**Short answer, no. There is not a "twist-chair."**


To convince yourself, it probably helps to make a physical model with a chemistry model kit. If you try to twist the chair, you can't do it without significantly moving at least one atom, in which case, the conformation is basically a "skew" or "twist boat." Try it.


The boat and chair conformations are indeed symmetric and achiral. The twist-boat or skew conformation has point group $D\_{2}$ and is indeed chiral.


A normal half-chair will have an axis of symmetry and is chiral.


An envelope conformation will have a plane of symmetry and thus be achiral.


I've found that some of the best depictions of six-member-ring conformations come from pyranose sugars. Because of the hydroxyl groups and oxygen atoms, there are [38 distinct conformations](https://en.wikipedia.org/wiki/Pyranose#Conformations) (2 chairs, 6 boats, 6 skew-boats, 12 half-chairs, and 12 envelopes).


From [Wikipedia](https://en.wikipedia.org/wiki/Pyranose#Conformations):



> 
> ![enter image description here](https://i.stack.imgur.com/WRLqW.png)
> 
> 
> 


Obviously, in less-substituted cyclohexane, there are fewer unique shapes, but it helps to see the different [ring-puckering](http://pubs.acs.org/doi/abs/10.1021/ja00839a011) or pseudo-rotation shapes.


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