So I've had this idea in the back of my head for a while, and a few weeks ago I finally downloaded Unity and made it. Right now all I've got is basically a tech demo:



Controls:
WASD to move
Hold shift to run
Press E to grab or let go of the cube or press the button
Hold control to lock the cube's gravity (not demonstrated in the video)
Right click to teleport (dev build only)

• The walls are colored based on their orientation. So all walls facing "north" have the same color, and all walls facing "south" have the same color, etc.
  
• The gradients between walls are curved ramps that you can walk up. When you walk onto a wall, your gravity changes so now you're falling toward that wall.
  
• The circle on the cube shows which wall it is currently attracted towards.
  
• When you carry the cube onto a wall, the cube's gravity undergoes the same change you just did. So if you rotated 90 degrees around the X axis, the cube's gravity rotates 90 degrees around the X axis.
  
• Hold control to lock the cube's rotation so it doesn't change (not demonstrated in the video)
  
• Push the button to set the cube's gravity to blue. It also makes a sound to let you know you pushed it (not included in the video).
  
• Oh yeah, and I still haven't figured out a good lighting solution. Using only ambient light looks fine, but the way that the gradients are rendered they turn to solid blue if I walk a few meters away from them.
  

I'll probably put it on GitHub if I do much more, but for now here's the latest Windows build. If you want to run it on Mac or Linux I could do that too.