"The center of the universe is, of course, that marvelous land known as Fraggle Rock. It is thus called because it is a rock and Fraggles live there. Fraggles are a noble race - fearless, dignified, intellectual. They represent the very pinnacle of civilization and culture. A Fraggle is most assuredly the best of all possible creatures."
An exposed portion of the Rock lies in a corner of the Gorgs' Garden. Although the Gorgs consider the Fraggles to be garden pests, they consider the Rock itself to be sacred, calling it "Kissing Rock." The Rock also extends under the garden to the Doozers' radish mines.
The Rock is a magical place, and one part opens into Doc's Workshop in Outer Space. The interior of the rock is centered around the Great Hall, which also contains the Fraggle Pond, whose water is supplied by Doc's pipes. Living quarters include Gobo and Wembley's Room, Boober's Hole, and Red and Mokey's Room. The Storyteller has her own home, with door and entranceway even, and Convincing John's Cave lays on the outskirts, past the paths used by the Doozers.
Behind the scenes
As explained in The Muppets Big Book of Crafts, the cave sets were made of modeling clay on chicken-wire frames. Producer Lawrence Mirkin explained in an interview that the sets were modular: they were built in pieces that could be moved around and recombined to create "a zillion different sets" at "twenty minutes' notice."