EDGE Extended is a port of the sequel to the original EDGE from Mobigame. Both games were very recently ported to the Android Market. I probably won't do a review of the original EDGE since the sequel is more or less the same, but with better puzzles and visuals. They're both simply fantastic puzzle games with unique mechanics and aesthetics, and I recommend both, but the sequel is definitely superior.
You control a simple rainbow colored cube and must navigate the very blocky world that you inhabit, collecting miniature cubes and finding the level exit. You can control the cube via special touch controls, buttons, or by tilting, and you make your way around by rolling over your sides in only four directions. Your cube can climb up single cube heights, and due to its shape and the nature of movement, you need empty space behind you in order to climb. If you get miniaturized to one third your size though, you can somehow climb up sheer walls.
You are rated on every level based on speed of completion and whether you picked up all of the various mini-cubes. The game gets more challenging and complex as you go along, and eventually you have to deal with switches, quickly moving platforms, ground tiles that fall after being stepped on, and more. You can even stick to the side of a moving wall by starting to climb it and then hovering there, but if you finish your climb or drop down too much, you'll fall. Occasionally the mysterious Dark Cube will show up, who seems to act as both friend and enemy, sometimes helping you along, and other times trying to murder you.
The visuals make this game stand out from any other. Despite being made up entirely of square shaped things, the world really feels alive. The visuals accentuate the game design as well, often throwing crazy optical illusions your way, forcing you to use the mini map to navigate these areas. The excellent electronic soundtrack is often very ambient, though it's quite varied. Some tracks sound straight out of Tron Evolution while others change the style up completely. Mobigame has the soundtrack available for free on their website, so you can check that out if you like it. You can download this great puzzler for only three dollars, and I highly recommend it. There is a demo of the original EDGE as well, if you want to test these mechanics out.