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Typically, the white cyclops requires the ring to be in the small inventory (which appears on the left side of the main screen) to appear. In this case, a white cyclops can appear immediately or after using one or more spells.

The white cyclopus wouldn't latch if you're wearing Violet or Ice Armor.

Also it wouldn't latch on if any of the normal cyclopus is already latched onto you. So the best way is to use area spells like Meteor Shower or Maelstorm to kill off the two normal ones, leaving the white one.

(Optional) Use Charm spell to make it latch on immediately.