The Calvin's 3x3x4 is a fully functional cuboid from Calvin's Puzzle. It features smooth layer rotations and a slightly scratchy feel, and it comes with the Tony Fisher logo on one side.
However, the most common of these upgraded Rubik’s Cubes is as simple as it sounds: like the 3x3, but bigger. The original puzzle has been expanded outwards to create bigger and more challenging alternatives: the 4x4, 5x5, 6x6 and 7x7.
It has a perfect cube shape but basically it's a Rubik's Cube twisted 45 o around a central axis, making 4 edge pieces become centre pieces, 4 centre pieces become corner pieces and so on. If you can solve the classic 3x3x3 you can't have problems with this one, just pay attention to the parity.
ON 12 SEPT 2012 TO BE RELEASED ... the cubes can be transformed into many other different shapes. ... Calvin's 3x3x5 Super X-Cube with Evgeniy logo Stickerless (Review)
The Mirror Cube aka Mirror Blocks. Many different types of Rubik’s Cube exist. Cuboids, different shaped puzzles (such as the Megaminx and Pyraminx puzzles), NxN cubes and more.
The Skewb (/ ˈ s k juː b /) is a combination puzzle and a mechanical puzzle in the style of Rubik's Cube. It was invented by Tony Durham and marketed by Uwe Mèffert. Although it is cubical in shape, it differs from Rubik's construction in that its axis of rotation pass through the corners of the cube rather than the centres of the faces.
Square-1. The Square-1 (previously called as Cube 21 and Back to Square One) is a shape-shifting three-layered twisty puzzle.