a.k.a. Pyraminx Cube
Purchased from Meffert's 2007.
(plastic, 2.2 inches)

Here is a photo of the other three sides:



It can be rotated along any of the planes that passes diagonally through the cube:



Jaap's Page credits this puzzle to Tony Durham, says that it was originally called the Pyraminx Cube by Uwe Meffert, that Douglas Hofstadter coined the name Skewb in a 1982 Scientific American article, discusses the relationship of the Skewb to the Pyraminx, and presents a solution. There are a number of variations of this puzzle, including the Skewb Diamond, Super Skewb Diamond, Skewb Ultimate, Skewb Kite, 3D Skewb, and Skewb Ball

Further Reading
Meffert's Page, from: http://www.mefferts.com/puzzles/skewbsol.html
Jaap's Page, from: http://www.jaapsch.net/puzzles/skewb.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/Skewb.htm
Dry Erase Board Page, from: http://www.thedryeraseboard.com/mechpuz/skewb/solution
A Cubist Page, from: http://www.acubist.com

Augmented Faces Skewb
a.k.a. Polymorphix Limited Edition
Purchased from Meffert's 2008.
(plastic, 2.9 inches)

Same as the Skewb where each face has a protruding piece on it. The colors of each of the four faces of a protrusion must match the color of the corresponding adjacent face, which gives an explicit constraint to the orientation of a face with respect to its corners.



Augmented Corners Skewb
a.k.a. 3D Skewb
Purchased from Meffert's 2008.
(plastic, 2.9 inches)

Same as the Skewb where each corner has been replaced with a protruding piece (that has the same three colors that match the adjacent faces).