The Flexible Hexagon by Tandem Toys
On the packaging I have with mine, it has in large letters "Betcha can't" as the title of the puzzle, with the Flexible Hexagon as a subtitle.
It's movement is quite horrible. There are not many possible shapes (maybe about 20 or so?) but they are hard to find because the movement is so counterintuitive. The first move at the ring shape will always be folding three of the hinges together inwards so that you form three pairs of tiles, pointing outwards from the centre. This can be folded open the other way to get the ring again but with the tiles in a different orientation, or in one other way to get some 3d shape.
I son't really know what the solution pattern is supposed to be. The solution shape is the 'paralellogram' as shown in Sandy's picture, but it is unclear what pattern there should be. The red/blue front is clearly used for the ring starting position, but the back has a red/blue/yellow/black design looking like cubes. The packaging says nothing about this, and I haven't yet been able to get a nice-looking pattern from it.