The Skewb, Skewb Diamond and Skewb Ultimate are all puzzles built on the same central mechanism : a 4-legged core with four out of eight similar pieces attached to it (and the other pieces free to move around it). Since these puzzles all function in the same way and only differ in their shape, they can be considered shape modifications of each other. This also means that pieces from any of the Skewb variants are compatible and can be interchanged. For example, two of Meffert's new puzzles, the 3D Skewb and the Polymorphix, are made by swapping the corner pieces of a Skewb and a Skewb Ultimate.
All of these puzzles can be solved with similar methods, although each one has a different set of pieces which must be oriented (for example, in a Skewb, the centers can be rotated freely without making the puzzle unsolved).
The Skewb is a cube-shaped puzzle. It consists of 6 center pieces and 8 corner pieces (four of which are attached to the central core). Unlike the Rubik's cube, which turns around faces, the Skewb turns around axes that go through its corners. It is a deep-cut puzzle - ie. each cut goes through the absolute center of the puzzle, and exactly half of the puzzle changes with each turn.
This puzzle was originally called the Pyraminx Cube by Uwe Meffert, but Douglas Hofstadter suggested the name "Skewb", and it has been called that ever since.
The Skewb Diamond is a octahedral modification of the Skewb. The Skewb Diamond has 6 corners (corresponding to the centers of the Skewb) and 8 centers (corresponding to the corners of the Skewb). Therefore, it can be made by truncating each corner of a regular Skewb and extending each center into a square pyramid.
The Skewb Ultimate is the dodecahedral version of the Skewb. The Skewb Ultimate has 6 of one type of piece and 8 of another type, corresponding to the Skewb's pieces, but the way they are cut is more complicated. This is the most difficult of these three puzzles, since in the Skewb Ultimate every piece must be correctly oriented for the puzzle to be solved.