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What is the point group of of cis- and trans-decalin?

enter image description here

I watched a video saying that it is $C_\mathrm{2h}$ for cis-isomer, but my friend says it is $D_\mathrm{2h}.$ I'm so confused.

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    $\begingroup$ D2h should contain quite a few mirror planes. Where are they? $\endgroup$ – Ivan Neretin Sep 5 at 8:04
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    $\begingroup$ Please edit to add a link to the video (link to your friend is not necessary). $\endgroup$ – Karsten Theis Sep 5 at 13:06
  • $\begingroup$ This video gets it right: youtube.com/watch?v=GERJoub3LVo $\endgroup$ – Karsten Theis Sep 5 at 16:02
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cis-Decalin

Here is a view of cis-decalin with the bridging C-C bond in the plane of the paper:

enter image description here

(It was made using the Jmol software, e.g. at https://chemapps.stolaf.edu/jmol/jsmol/simple.htm using the "Load by name" button and entering "cis-decalin".) At https://www.chemtube3d.com/stdecalinflips/, you can see that this can flip into the mirror image (much like a cylcohexane chair flip).

What is the point group of of cis-decalin?

I see a two-fold axis (perpendicular to the paper). I don't see a center of inversion or any mirror planes; the molecule looks chiral (the flip mentioned above changes it to its mirror image). So maybe C2?

trans-Decalin

Here is a view of trans-decalin with 5 carbons closer to us and 5 further away from us:

enter image description here

I see a center of inversion, a mirror plane (left:right swap), and a two-fold horizontally in the plane of view. I guess that's C2h.

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    $\begingroup$ Related: Does trans-decalin really have a plane of symmetry? Trigger warning: You might be watching the gif forever... $\endgroup$ – Martin - マーチン Sep 5 at 14:11
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    $\begingroup$ I have run some conformational checks on the structures. The maximum point group for cis-decalin is as you propose C2. For trans-decalin, we do indeed find C2h as already stated. There are other (higher-energy) conformations with twist-boat rings in their conformations, which (mostly) would be of C1 symmetry. $\endgroup$ – Martin - マーチン Sep 6 at 9:25

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