I had not intended to create an instructable about it, but was told that I should. I now wish that I would have taken more pictures of the process, but alas, these are the only decent ones I have.
The tardis is made of 8 small boxes, laid out in two stacks of four. Each stack has an axle running through the corner, so that it can open up like a fan. To open the box, only the top level need to be moved. The top three levels of boxes (the bottom level being stationary) have pegs on the bottom that pull the lower boxes out. Once the top box has been turned to a certain angle, the peg catches on the next one, pulling it out as well. This also works in reverse, allowing the box to be closed entirely by only turning the top level.
I hope you enjoy it!