You Do Need power plug adapter while traveling from Cocos (Keeling) Islands to Vatican City.

Here is Why You Need An Adapter

The outlet and plug type used in Vatican City are C, F and L and in Cocos (Keeling) Islands is I. This is how they look like.

In Cocos (Keeling) Islands, outlets of type I are in use.

Type I

In Vatican City, outlets of type C, F and L are in use.

Type C

Type F

Type L

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