Princess Patricia's coronet would likely be identical to her sister's which is now in Livrustkammaren, The Royal Armoury museum in the Royal Palace in Stockholm. (link)
It was made of gilded silver by Garrard in 1901 and worn the next year. Interestingly, the website states that Victoria Patricia Ramsay was a brukare (user). Crown Princess Margaret must have loaned it to her sister at some point, which leaves the question of what happened to Patricia's.
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