The dome housed a train that took you right to Metropol, the city of glass and light.
Let's just hope it lives up to the advertisements.
TIP: After visiting a location once, you can use the map to fast travel around the city to save yourself the trouble of walking.
Unlike normal walkthroughs, in Nice Game Hints you can select just the puzzle you want hints for. Here are listed the puzzles for "Part 5 - The city of Metropol" in Primordia. The guide you choose only contains information about that puzzle, reducing possible spoilers for other puzzles.