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It is reported that iodine forms compounds like $\ce{(CH3COO)3I}$, $\ce{I(ClO4)3}$ and $\ce{IPO4}$ which contains $\ce{I+}$ and $\ce{I^3+}$ and are not bonded covalently as in interhalogen compounds.

Generally, Halogens form anions of the type $\ce{X-}$ to achieve stability by attaining noble gas configuration. However iodine loses electrons when it forms a cation and does not attain noble gas configuration. So why does iodine form cations while no other halogen does?

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  • $\begingroup$ Why should iodine not form cations? Fluorine cations can be supplied (albeit not stable for extended periods of time). Thus, any atom can likely form cations, although it is unproven for helium and neon as far as I know. $\endgroup$ – Jan Nov 13 '15 at 16:51
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    $\begingroup$ You should check your data - all three compounds are covalent. Doubt if you can find any solid data on any +3 cation which isn't coordinated to ligands. $\endgroup$ – Mithoron Dec 14 '15 at 1:44
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Iodine is the biggest halogen and by extension the most polarizable.

Diatomic iodine can be oxidized with nitric acid to facilitate electrophilic aromatic substitution.

Iodide ion, as found in sodium iodide, can also be oxidized by concentrated household bleach to facilitate EAS as well.

In the examples you give, there are strong electron withdrawing groups (such as oxygen, which is found in each of your examples). It is plausible that the oxygen has stripped the iodine of its electron(s) in each of your examples.

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