The Dotted Hole is a cave in which you get the Sapphire or the Ruby, enabling trade with the respective games. You get in by using Cut on the door after you help Lorelei defeat the three Rocket Grunts at Icefall Cave. You navigate the cave using Braille, the language for the blind that uses tangible dots to communicate, thus the name.
Once you get to the floor of the item, a Rocket Scientist steals it, and you'll need to backtrack to Chrono Island to receive it.
Source: Experience
