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An 11x11x11 cube has 11 layers in every direction and 602 visible pieces. Solving one is more of a long session than a quick solve, and 11x11 is not a WCA event. These puzzles are mostly chosen by cubers who have already mastered smaller big cubes and want to test themselves on something bigger, and by collectors. In this category you will find 11x11 cubes from manufacturers with years of experience making big cubes: MoYu, YuXin, QiYi, ShengShou and DianSheng.
With an 11x11, the differences in size are much greater than with a 3x3. According to manufacturer and distributor data, the YuXin Little Magic 11x11 measures about 110 mm and weighs over 800 g. The YuXin HuangLong 11x11 V2 and the QiYi 11x11 measure about 85-88 mm. The smallest is the MoYu MeiLong 11x11 V2: about 70 mm and just over 200 g. A small, light cube is less tiring for your hands during long solves, but its pieces are tiny. A bigger one makes it easier to grip several layers at once, but after a few dozen minutes you will start to feel its weight.
In a big cube, magnets help the layers "snap" into place, so they are less often left slightly misaligned. Misaligned layers are the main cause of lockups, i.e. turns getting blocked. The DianSheng Galaxy M 11x11x11 was the first factory-magnetized 11x11. Magnetic versions are also available for the HuangLong 11x11 M V2 and the SengSo MoSheng Cubic 11x11 Magnetic. The MoYu Meilong 11x11 V2 M Core-Ball and the QiYi Magnetic 11x11x11 Ball-Core also have magnets in the central ball (core), which pull the pieces from the inside and stabilize the whole mechanism while turning. Non-magnetic versions are cheaper and lighter. They also work well with calm, precise turning, but you need to align the layers more carefully.
An 11x11 is not a good first cube. It is solved with the same method as a 4x4 or 5x5, i.e. by building centers and pairing edges, it just takes much longer. That is why it is good to have at least a 5x5, and ideally a 7x7, under your belt. If your 11x11 is meant to be a challenge for a few evenings or a shelf display piece, a non-magnetic model is enough, for example the Little Magic or the classic ShengShou. If you plan to solve regularly and time yourself, you will appreciate a smaller size and magnets, and a Ball-Core version will give you the most stable feel.