Why is cyclooctateraene shaped like a "tub" rather than a "chair"?

I understand that for cyclooctatetraene (COT) to "escape" the horrible prospect of becoming an anti-aromatic molecule, it must [adopt a non-planar conformation](http://www.masterorganicchemistry.com/2017/03/27/antiaromaticity/).


[![enter image description here](https://i.stack.imgur.com/k9gMy.png)](https://i.stack.imgur.com/k9gMy.png)


The widely touted conformation of COT is said to be "tub" shaped. My sources (random links Google threw up) also concur on this particular "tub" conformation.


**But why isn't it "chair" shaped instead?**


Going along the same line of cyclohexane (non-aromatic), wouldn't a "chair" conformation reduce (even if it's a little bit) the steric repulsions due to crowding of hydrogens atoms on one side/face of the molecule?


Or even if "avoiding steric issues" isn't really the big idea here, then I could re-phrase my question as:


**What stops COT from assuming a "chair" shaped structure?**


The "chair" structure that I have in mind for COT is something like this:


[![enter image description here](https://i.stack.imgur.com/ntITg.jpg)](https://i.stack.imgur.com/ntITg.jpg)


(*I don't have access to a decent enough organic chemistry sketcher to have this drawn any better, sorry.*)




It's all about the 3D structure of double bonds.


If we look at the tub form we see that all dihedral C-C=C-C angles are 0°. the C=C-C angles are 125°, also pretty close to the optimal value. Everything works out fine, there's basically no strain on the whole molecule.
[![enter image description here](https://i.stack.imgur.com/08GAP.jpg)](https://i.stack.imgur.com/08GAP.jpg)


I tried to build the chair form of all cis, but every optimization ended up in either the all cis tube form or the cis-trans-cis-trans chair form. The best structure that looks like the all cis chair form I ended up with is this:


[![enter image description here](https://i.stack.imgur.com/sXpae.jpg)](https://i.stack.imgur.com/sXpae.jpg)


First of all, it's pretty flat, so antiaromaticity would again play a role and the dihedral angles are also ~33° for the double bonds in front and in the back, which is energetically quite bad and unstable.


The cis-trans-cis-trans compound is definitely no monstrosity. I'm working a lot with trans-cyclooctenes and I don't see why this shouldn't be possible if a trans,trans-cycloocta-1,5-diene is possible. 


[![enter image description here](https://i.stack.imgur.com/bR5G6.jpg)](https://i.stack.imgur.com/bR5G6.jpg)


Here we've got 0° for the dihedral angles for the cis bonds and 125° for the trans. Yes, this is far away from the optimal value of 180° but quite similar to what you expect from trans-cyclooctenes (around 135°). I feel like it would be quite reactive and unstable but it could definitely exist. There's just no good way to produce it I guess.


So overall: all angles in the tub form are much closer to the optimal values than in either chair form and the all cis form is quite planar.


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