What do you think it would be like to walk through a structure shaped like a Menger Sponge 3D fractal?

Assuming that such a structure could be built that could safely hold people in it. Three or four iterations of the design process should be enough to make it interesting. I thought It might be a fun and educational idea for a museum. It is one thing to look at a 2 dimensional fractal, but it would be something else to have to travel inside of a 3D one. I am not sure what would be the best way to get from one level to the next. There could either be stairs on the outside of the cubes or you could pull your way up like a 3 dimensional jungle gym. What do you think a cat would think of such a structure?