The Megaminx is not cube shaped. Nor is it built on a cube core. It does not have the same number of pieces as a 3×3×3 cube. So why do I include it with the Specialty 3×3×3 Cube-like Puzzles? Because the strategy I use to solve it is more like solving a cube than any of the other cube-like puzzle strategies I employ.
You can think of a cube as having 3 layers of edges. Bottom edges, middle edges, and top edges. There are 4 edges in each layer of a cube. There are 5 edges in the top layer of the Megaminx. Also 5 in the bottom layer. There are 20 edges in the middle section of the Megaminx. 5 in the bottom half, 5 in the top half, and 10 around the middle. But all 30 edges of the Megaminx can be solved like the 12 edges of the cube. Here’s how it works. Just like you can solve a cube by starting with the white edges, you can start the Megaminx with the 5 white edges. Then all 20 edges in the middle section can be solved in ways like either the 5 whites or like the middle layer edge pieces of a cube. Basically you either put an edge directly in place, or use Up-Replace-Down. For the last 5 edges they can be solved like the top edges of a cube. I start by flipping those that need it, then I put them in place. F U R Ui Ri Fi or F R U Ri Ui Fi, or something very similar, to flip two edges. Then a variation of R U Ri U R U2 Ri to put them in place. Since there are 5 edges instead of only 4 it isn’t always U or U2. It helps to understand how these moves work on a cube so they can be adapted to the Megaminx.
Sometimes I like to solve the Megaminx edges first. Then I solve all 20 corners using setup moves and the Up-Replace-Down 3-Cycle. mm-hm. It usually takes 9 or 10 3-cycles if I can solve two corners at a time.
Sometimes I solve the 5 white corners along with the 5 bottom half middle edges using F2L techniques.
Sometimes I solve the 10 middle corners using basically the same F2L technique. That is, I solve each one along with an adjacent edge. The lower middle corners I do with a middle edge. The upper ones I do with a top half edge.
I use the Up-Replace-Down 3-Cycle to get the unsolved corners in the top layer after all the rest of the Megaminx is solved. Sometimes I have to twist top corners at the end, and use the same technique I use to twist two corners of a normal cube.