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What is the number of optical isomers for this compound?

Also, there seems to be no clear-cut boundary between geometrical isomers and optical isomers. Referring to a post in StackExchange,

is (RS)- and (RR)-form of 1,2-dichlorocyclohexane considered optical isomers or geometrical isomers? The isomers exist due to restriction of rotation caused by the ring, you can also called the two geometrical isomers, can't you?

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    $\begingroup$ Please specify how you intend to isomerize the drawn molecule: If you exchange only the halogens amongst themselves, you have the same situation as in the methane derivative CFClBrI. If you allow exchange with the hydrogens, it gets complicated. $\endgroup$
    – TAR86
    Jan 10, 2019 at 5:02
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    $\begingroup$ @TAR86, he's talking about stereoisomerism, not structural/constitutional isomerism. One has to predict number of optical isomers of the given compound, without playing around with the basic skeleton. $\endgroup$
    – esoteric-elliptic
    Jan 10, 2019 at 6:17
  • $\begingroup$ I think that you are over thinking. As enantiomers do not superimpose each other obviously they haven't the same geometry. When discussing enantiomerism you are already further. It is just that at a first glance they might look the same, but enantiomers certainly have different geometry. You can call them "geometrical isomers with optical activity" but "enantiomers" do it better. $\endgroup$
    – Alchimista
    Jan 10, 2019 at 8:28
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    $\begingroup$ The question for this molecule is heavy constrained because the molecule is essentially rigid and there is no meaningful way to "swap" the stereochemistry at any individual centre. The carbon core is the same as adamantine and it isn't called that for nothing. However the overall molecule has the same stereochemistry as the (equally rigid and tetrahedral) methane so generates just two enantiomers with 4 different halogens. $\endgroup$
    – matt_black
    Jan 10, 2019 at 17:43
  • $\begingroup$ Dammit editor. Adamantane not -ine. $\endgroup$
    – matt_black
    Jan 10, 2019 at 17:58

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1-Bromo-3-chloro-5-fluoro-7-iodoadamantane would be an interesting example of central tetrahedral chirality without the actual (physical) center. Exchanging halogen atoms will result in only two stereoisomers.

Due to its rigidity, its stereochemistry is related to tetrasubstituted tetrahedrane (tricyclo[1.1.0.02,4]butane; or rather its imaginary geometrical model, because it would be very strained and unstable), whose stereochemistry is related to bromo(chloro)fluoro(iodo)methane.

Fig.1

To your additional question: It depends how (far) you'd like to go with removal of the rotation restriction, anyway the resulting compounds will already not be original 1,2-dichlorocyclohexane.

Fig.2

I mean yes, (1R,2R)-1,2-dichlorocyclohexane and (1R,2S)-1,2-dichlorocyclohexane can probably be considered geometrical isomers (in addition to optical), they can even be named trans-1,2-dichlorocyclohexane (which has two enantiomers, the other one being (1S,2S)) and cis-1,2-dichlorocyclohexane; but this isomerism is not caused by rotation restriction, but by different arrangements on chiral tetrahedral carbons.

But note that geometrical isomerism is usually used in relation with double bond cis/trans isomerism; and together with optical isomerism are both deprecated terms.

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