Odd/Even swap rule for chiral compounds in stereochemistry I had this question asked in my exam, where I was supposed to find if this pair is a diastereomer:

Now, I have learnt this rule where: Making odd number of swaps in a molecule means they both are enantiomers, and making even number of swaps means they are identical.
So according to this rule, I made even no. of swaps in the molecule to the right, which means it is identical to the inital molecule that was on the right. Now this newly formed molecule superimposes the molecule to the left perfectly. Hence, in my opinion the two molecules in the picture above should be identical. But the answer given in my answer key is that they are diastereomers, and not identical.
Is there any flaw in my justification?
While this rule is certainly not infallible, it is often used in organic compounds, especially for Fischer projections.

The odd/even rule implies that no change of configuration occurs if an even number of swaps are made at a single chiral center and change of configuration occurs if an odd number of swaps are made at a single chiral center.

Here, you have made 3 swaps at both ends which means you changed the configuration of 2 out of 4 chiral centers. Hence, you can make the inference that 2 chiral centers (C-2 and C-3) are the same, while another 2 (C-1 and C-4) are different. These are hence diastereomers.

I am assuming that you thought you made 3 + 3 = 6 swaps, so the compound should be identical. But the odd/even swap rule is only applicable to a single chiral center, hence the error.

Finally as pointed out already, this rule doesn't apply anywhere where the central atom doesn't have a tetrahedral geometry. As counterexamples, coordination complexes often have non-tetrahedral geometries:

octahedral: $\ce{[Co(NH3)6]^3+}$
square planar: $\ce{[PtCl4]^2-}$
dodecahedral: $\ce{[Ce(NO3)6]^2-}$

Note that these specific examples are optically inactive but by changing the ligands for different ones, it is possible to create optically active versions with the given geometries.
However, since organic chemistry mostly involves tetrahedral carbon as the chiral center, the rules certainly do apply there.