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Once a regular Megaminx stops being a challenge, the next step is a bigger minx. This category has dodecahedral puzzles larger than the Megaminx: Master Kilominx, Gigaminx, Elite Kilominx, Teraminx, Petaminx, Examinx, Zettaminx and Yottaminx. They share the same shape, but each face is divided into more layers. That is why they take longer to solve and need more focus.
The easiest way is to compare them to cubes. The Megaminx corresponds to a 3x3 cube, and the following models are dodecahedral equivalents of bigger cubes:
Models with "Kilominx" in the name are even-layered. They have no fixed face center, so just like on a 4x4 or 6x6 you have to work out the position of the centers yourself. On odd-layered models (Gigaminx, Teraminx, Petaminx and bigger) the center of each face is fixed, which makes orientation easier. All of these puzzles are solved with the reduction method: centers first, then edge pairing, and finally like a regular Megaminx. If you can solve a Megaminx and know reduction from bigger cubes, you can manage without learning a new method.
Many models come in a magnetic version, marked with the letter M or the word Magnetic in the name. Examples include the YuXin Huanglong Master Kilominx M, DianSheng Gigaminx M and DianSheng Galaxy Magnetic Petaminx. With so many layers, magnets really help: the layers "snap" into place on their own, so you need to realign them less often and get fewer lockups. The DianSheng Galaxy Gigaminx Ball-Core also has magnets in the core that stabilize the whole mechanism. Non-magnetic versions are simpler and usually cheaper. They work well for relaxed solving too, but turning them requires more precision from the cuber.
After the Megaminx, most people choose the Master Kilominx or the Gigaminx. They can be solved in a reasonable time and are great for learning reduction on a dodecahedron. The Teraminx and Elite Kilominx mean noticeably longer sessions. The Petaminx and bigger models are puzzles for fans of really big puzzles and for collectors rather than for everyday practice. This category includes minx puzzles from ShengShou (SengSo), YuXin Huanglong and DianSheng Galaxy, and many models are available from several manufacturers. This lets you compare the same size in a classic and a magnetic version, as well as successive generations such as the SengSo Gigaminx V3 or SengSo Teraminx v2.