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Cyclodecapentaene

I think that the above structures are identical compounds as I doesn't exist in the shown form but it would exist naturally in the II form, so these should be identical.

But these are mentioned to be geometrical isomers in a book that I was reading. Even if I assume that I existed in it's given form, then how can they be geometrical isomers? In I, there are two trans alkenes, three cis alkenes and in II, all five are cis alkenes.

So, are these compounds isomers or identical?

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    $\begingroup$ Both I and II (and there are more) are mere projections of a 3D molecular structure onto a 2D plane; shadows of the Plato's Cave, or an impression of a Flatland's citizen of an object from our world. Cyclodecapentaene does possess geometrical isomerism, and I and II are indeed isomers, but to get an idea how it works you need to think in 3D and think stability in terms of angle strain. $\endgroup$
    – andselisk
    Nov 2 '20 at 8:04
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    $\begingroup$ Seriously and chemistry let apart, you can't compare existing X to non existing X' and claim there to be identical. $\endgroup$
    – Alchimista
    Nov 2 '20 at 8:53
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    $\begingroup$ Well, you can tell that two groups are trans vs all-cis and that cis-trans is isomerism, so what's the point of the question? $\endgroup$
    – Mithoron
    Nov 2 '20 at 13:57
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If you make spring-and-ball models of both compounds, you can see that the two compounds are entirely different, and both are contorted.

enter image description here

The all-cis model on the left has all its hydrogens pointing outward, so the contortions of the carbon chain involve just carbon-carbon twisting to come close to 120 degree angles. The model of the cis-trans molecule on the right has two inward-pointing hydrogens (all the rest point out) which are sterically interacting so much that they introduce strain that is not evident from the carbon-only diagram in the original post. (If I put in all the hydrogens, the image is too cluttered.)

The fact that one is all cis and the other cis-trans certifies that the molecules are different, but the 2-D drawing can seem vague. The NMR spectra of these two compounds would be different. I can imagine the molecule on the left flipping all around (the model sure did!), but the molecule on the right seems pretty stuck.

Thinking in 3-D is easy after you've done it many times. But when you are starting out, it is helpful to make molecular models. And even if you've done it a million times, there are situations where your mental image is so fluid that you need to solidify it with a model, no matter how inadequate the model is. And then you mentally add onto the solid model.

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