Jaitea said:
Sorry but I think when you watch the movie you get the feeling the freezing chamber IS in the main body of the city and not on the vane. When Luke gets sucked out the window he 'luckily' lands on the vane. The sudden reappearance of Vader whilst Luke was walking through the corridor of the vane makes you think shit how did he get there! Makes you jump! It just doesn't make sense that when Luke got separated from Artoo that he had such a long journey to face Vader (in a few seconds!!) or those seconds robbed.

Wherever the freezing chamber is we know for certain that the area where Luke is thrown out of the window is in the vane and when Vader resumes his attack leading to the final tumble it's also in the vane.

There is a strong case for the freezing chamber also being in the Vane but it's never made 100% clear and it doesn't need to be.

Ady has posted that he believes that the chamber is in the Vane and explained how he thinks Luke gets there and moves around it but he has also said he doesn't need to show that in the edit.