Variomatic Cube is a twisty puzzle with gears. All three pairs of opposing faces are connected by gears. And they are not just some gears, they are gears with a varying gear ratio. Some sometimes, opposing gears will turn with a 1:1 gearing ratio, some with a 1:2 ratio, and sometimes with a 2:1 ratio. The operation of the variable-ratio gears is explained and illustrated here and here. Watch a demo of the inner gearing mechanism here.
The name of this puzzle is a tribute to the variomatic transmission system by the Dutch car manufacturer DAF. Note that the variable-gear-ratio mechanism is very different from the DAF variometic system.