Half Truncated Cube
The half truncated cube is a modification to the standard 3x3x3 cube. The truncation is much greater than you see on a Cuboctahedron. As a result there is some minor shape-shifting during scrambling and solving. The impact on your ability to solve the puzzle is not affected any more than it would be with an Octagon. You do get two shapes for corners but it isn't tricky to 'see the original cube' when you are solving this puzzle.
If you are good with your hands, you can make one of these yourself and buy stickers online. If, like me, you're not (see the home-made bandaged cubes if you want to see how bad), you have to rely on finding someone else who has done the modification and is selling at a reasonable price. If you aren't making one of these yourself then it's probably best to regard it as a collector's item only. It's a lovely looking modification but no great challenge as a puzzle.