Concept
The Axis Cube (or Axel Cube) is a modification of a standard cubic 3x3. The way it's designed can be deduced from its looks and the correlation to a 3x3, but can be pretty tricky to people who see this for the first time. In short: it comes down to rotating the cube by 60°, cutting the faces and extending them to make the puzzle cubic again. With this in mind, you can easily see that this is just a shape modification of a 3x3 and is solved in exactly the same way.
The concept was first introduced by Adam G. Cowan (the same person who designed the Ghost Cube in 2008).
Solving Method
Since this is essentially a shape mod of a standard 3x3, the way to solve it is exactly the same. Every method which is used to solve the 3x3 can be applied to the Axis Cube. But there are some difficulties.
One way to approach the 3x3 is solving it layer by layer, working your way from bottom to top. This is, in my opinion, the easiest way to solve the Axis Cube as well.
Speedcubers use F2L for solving the first two layers at a time. This is possible as well, but can be tricky and confusing on the Axis Cube, since shape is more important than color when it comes to making corner-edge pairs. The ways speedcubers use to solve the last layer is also applicable to the Axis Cube, but orientation of pieces can be deceptive.
Some people solve a 3x3 by putting in all the corners (with its correct orientation) first and than solve the edges. This is an interesting way to solve the Axis Cube, but a true understanding of the looks of the Axis Cube is needed when you want to approach it like this.
One thing to keep in mind while solving an Axis Cube, is that center rotation has a meaning. So it's essentially a Super Cube. Whatever the method is you use to solve it, the rotation of the center pieces is important and the approach you use should be adapted to this concept.
I could go on for a while but it all comes down to the same conclusion; the Axis Cube is solved in exactly the same way as a 3x3, but has its difficulties due to different shapes. Try some to see what appeals you the most. But more importantly: try some to see which one challenges you the most!
Personal Experience
The Axis Cube was my first shape shifting puzzle ever. I was just getting comfortable with the regular 3x3 when I decided I wanted some new challenges. With this in mind, I bought an Axis Cube and a Megaminx, which are essentially solved like a 3x3.
Even tough I could solve a 3x3, it took me a while to bend my perspective and solve the Axis Cube.
The looks of it are, simply said, terrifying when you see it for the first time (especially as a newbie in the broad world of twisty puzzles).
Nevertheless, I enjoyed every bit of the solve and I'm glad to have it in my collection. It's one of those puzzles I grab for a quick and fun solve.
Source: http://twistypuzzles.com/
Source: http://twistypuzzles.com/
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