The Dome Fossil was one of the two fossils available to Red, Alice and Abe during their trip sthrough Mt. Moon early on in the game, which was chosen by both Alice and Abe. The other option was the Helix Fossil which was chosen by Red. The Dome Fossil was considered the counterpart to the Helix Fossil, being the dark to the Helix's light in terms of Lore. Kabuto is the pokemon that is recovered from the Dome Fossil if chosen and reanimated on Cinnabar Island late in the game,
Near the end of the Mt. Moon cave Red was unable to progress to the exit of the tunnel before choosing one of two fossils that blocked the path to the exit. As mentioned the choices were the Dome Fossil and the Helix fossil. Red opted to choose the Helix Fossil which soon became a symbol of chaos and the official mascot of Anarchy, while the Dome Fossil represented Democracy (or Domecracy as it was referred to by Helixists) and was blamed for all the unfortunate events that occurred to red throughout the journey such as pokemon being released.
As of the Randomized Firered Playthrough, however, a less evil interpretation of Dome has arisen. As Alice picked the Dome Fossil as opposed to the Helix Fossil, it is believed that neither Dome and Helix are evil, but different sides of the same coin. As the world was far too chaotic, it required order and Dome, which is why Alice chose it.
Disciples of Dome
Randomized Fire Red
In Gen 3.5, the Dome Fossil was revived into Lwweekjjje, an Ariados with the ability Sand Veil.