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"I just finished building them before you had your, well, episode."
Redirection Cubes can be placed on Cube Buttons, but this never occurs in the game.
One side of the Redirection Cube has a second, smaller lens (presumably to help focus the beam) in front of the normal lens, with the other five sides featuring only one lens.
When a Thermal Discouragement Beam makes contact with the cube, it is redirected through the marked side. When the cube is picked up, this "output" side is turned forward if possible, to better assist aiming redirected beams.
According to GLaDOS, the Redirection Cubes were to be tested for the first time shortly before Chell made her first escape.
In the Cooperative Testing Initiative, guiding a Thermal Discouragement Beam into a receptacle will automatically "snap" to the center of it if it's close enough, making the process slightly easier. This feature doesn't exist in Singleplayer.
Redirection Cubes do not have a alternative texture for when they are on a button. This is because the cube has no blue light-up areas in the first place.
Behind the scenes
The Redirection Cube was first introduced during the Portal ARG, in one of the ASCII art images given by the BBS, that later appeared to be a diagram depicting its use with a Thermal Discouragement Beam, as revealed by the April, 2010 issue of Game Informer. During then, it was named as a Weighted Pivot Cube.
An updated and moving diagram was revealed during E3 2010.
The original Thermal Discouragement Beam diagram, showing a burning Sentry Gun.
ASCII art version.
Weighted Pivot Cube flying among other objects through a Pneumatic Diversity Vent.
Updated Thermal Discouragement Beam diagram, showing a Sentry Gun cut in half.
A Weighted Pivot Cube on the floor, with a Thermal Discouragement Beam working above.
A Weighted Pivot Cube being propelled by an Excursion Funnel.
Weighted Pivot Cube redirecting a Thermal Discouragement Beam at a Sentry Turret, making it explode after setting it on fire.
Weighted Pivot Cube being placed on a Super Button.
Closeup of a Weighted Pivot Cube redirecting a Thermal Discouragement Beam.