Circle of Regality

The Circle of Regality is the Royal Wraith's elliptical crown, found on sublevel three of the Royal Wraith's Palace. Being made of pure gold and encrusted with amethyst gems, it weighs quite a bit, needing one hundred Pikmin to carry it. However, since only Purple Pikmin will be available, it only requires ten Pikmin. Despite what the ship says, it is an ellipse, not a circle. To get it, the Royal Wraith must be defeated.

Olimar's journal

 * "Today, my Pikmin and I stumbled into a dwelling with lots of regalia and the color purple. We faced off against several monsters to get through the cave, such as a purple arachnorb and an emperor bulblax. Then we came upon the self-proclaimed king of the wraiths, the royal wraith. My Pikmin were also turned purple upon entering the arena. After beating the king, the Pikmin picked up this obscure crown. What it is made of, I don't know..."