What is the number of hydrate isomers of chromium(III) chloride hexahydrate?

Assuming $\ce$ is an octahedral complex, the answer should be four as there can be $0, 1, 2$ or $3$ $\ce$ ligands inside the coordination sphere. However, numerous sources say the number of isomers is three discarding the case with three $\ce$ ligands inside the coordination sphere. Only Loong's answer and another answer in a linked question say otherwise acknowledging the existence of the isomer with three $\ce$ ligands within the inner sphere. Every other place simply states that only three isomers have been experimentally discovered. Also, in coordination isomerism too, in the case where both spheres become uncharged is ignored. What is the reason?

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Regarding the coordination isomerism question, the reason why it's not considered as an isomer in the case of two uncharged complexes, is that there is no ionic attraction. The two coordination spheres should act as individual ions and hence participate in the ionic sphere. But in this case, where the two spheres carry no charge, there isn't a force, namely the electrostatic force, which binds the two spheres.

Your question on CrCl3.6H2O is a very debatable topic and there hasnt been a unanimous decision that has been put forth by all the authors. Some say there are 3 or rather most of them say 3, only one author, JD Lee says that there are 4.

The reason given by the authors to support there claim of only 3 isomers is not very concrete, but it still majority of the authors believe that it is true. The H2O that exists outside the coordination sphere is the water of crystallization. The water of crystallization is believed to be present within the voids created by an anion and a cation. Now if the isomer [CrCl3(H2O)3] 3H2O should exist then it must have these voids. But here there isn't any anion in the ionic sphere, in fact it is believed that there isn't any ionic sphere. Therefore this isomer doesn't exist and hence cannot be the 4th isomer.

Now, it's also believed that the H2O is actually held to the central metal atom (Cr) with the help of dipole forces and that the voids are not needed. So that would mean that this exists and since it is theoretically an isomer, it should also be an isomer practically.

That brings us to to this very important question, what is the significance of the water in the ionic sphere? Now most books say that it's the water of crystallization of that compound. So if the water of crystallization must be present in the voids so that they can be removed by physical processes like heating, the 3H2O wont be an isomer anymore, but just another compound that exists with the same molecular formula.