What is a Skewb?

The word "Skewb" comes from "skew" and "cube", and it is the name of a mind boggling little toy. Its base components are four corners fixed to the axes of a tetrahedra, six squares which each sit between two of the mentioned fixed corners, and four lose corners which sit in the other four gaps between these six squares. The cube which results from this construction looks like this:

Each twist of one corner will move half the surface of the skewb by 120°. You twist corners, not sides. That's why I prefer looking diagonally at the skewb, with two corners pointing towards me ("Top Front" and "Bottom Front", for the non-picture readers).

Imagine that you would rotate the "Bottom Right" corner clockwise: The "Top Right" corner would then move into the "Bottom Back" position, the Right front square would move to the right back, The "Bottom Front" stone will move to the "Top Right" position, and the "Bottom Back" corner will end up in "Bottom Front".

How to master this devilish little thing:

If you own a skewb which is in disorder, do not try to "clear up" one side of the cube after the other. Instead, try to understand how this thing works and you will find that there is less chaos than you thought at first glance.

1. Locate the four "fixed" corners, those which are sitting on the main axes of the skewb. You can find them by lightly pressing on the centre of the corners. If they do not move inwards, they are fixed and sit on an axis. If they move, they are lose stones. Let one of these "fixed" stones be "Top Back", then the other fixed ones must be "Top Front", "Bottom Left" and "Bottom Right". Anything else is impossible.
2. "Top Back" and "Top Front" have one colour in common. Always. If they don't, something must be wrong with your skewb, or you must live in a strange other universe. The orientation of these corners does not matter at all! They only have to sit in the correct position. Also, ignore the centre squares.
3. Next, check "Top Left" and "Top Right" if they have the correct matching colours. Again, orientation does not matter at all, only the correct position does. If you have to correct anything, you only need to twist by rotating around the "Bottom Left" and "Bottom Right" axes. Leave the fixed corner stones in their place.
4. Now, all corner stones are in their correct positions, yes, even the bottom stones. Everything else is impossible. Why? The "lose" corner stones have the same logical rules for their movement as the "fixed" ones. Yep: It was not necessary to find out which corners are fixed on an axis and which ones are lose. But knowing that these stones are fixed on an axis has helped you a lot to understand the logic of the skewb: There is less chaos in it than you thought!
5. Correct the corner stone orientations: Hold the skewb in a way that a corner stone, which is wrongly oriented, sits in position "Top Front". Now be careful, do not turn the skewb, do only twist corners. And here I need to explain my skewb notation system: "BR" is the "Bottom Right" corner, "BL" is "Bottom Left", and so on. "+" is an anticlockwise twist, "-" goes clockwise. Ask a math freak why this is so, I just use it like this because they defined it that way.
   To make TF change its orientation clockwise:
   BR+, BF+, BL+,
   BR+, BF+, BL+,
   BR+, BF+, BL+
   Effect: TF/(-), BL/(-), BR/(-)
   To make TF change its orientation counterclockwise, TF/(+), you will have to twist:
   BL-, BF-, BR-,
   BL-, BF-, BR-,
   BL-, BF-, BR-,
   Effect: TF/(+), BL/(+), BR/(+)
   
6. Now turn the skewb to the left until the next wrongly oriented corner stone sits in "Top Front" and repeat. Do not turn the skewb over, make sure that "Top" always stays "Top".
7. All Top corner stones have correct orientation? OK, now turn the skewb over and repeat the same thing for the (former) bottom side.
8. All corner stones should now sit in correct places and have correct orientation, but I bet that most centre squares will sit in wrong positions. What to do? Well. Let's assume they have the following Numbers:
   • Top is 1.
   • Front left is 2.
   • Front right is 3.
   • Back left is 4.
   • Back right is 5.
   • Bottom is 6.
9. Now you can check or simply try if one of these combinations could help you:
   • Twelve twists to move five centre squares in a circle.
     Orientation of the corner stones is unaffected:
     BR+, BL-, BR+, BL-, BR+, BL-,
     BR+, BL-, BR+, BL-, BR+, BL-
     Effect: 1/1, 2/6, 3/4, 4/2, 5/3, 6/5
   • Nine twists to move all 6 center squares and leave all corners untouched. After this operation, the skewb will appear to be turned, because square 1 moved, and we kept it "on top" all the time. Confusing? Try it out!
     BR+, BF+, BL+, BB+, (BB is "Bottom Back")
     BR+, BF+, BL+, BB+, BR+
     Effect: 1/5, 2/4, 3/2, 4/6, 5/1, 6/3
   • Four twists which will change the positions of 3 centre squares. Four corner stones will lose their orientation, but not their position:
     BR+, BL-, BR-, BL+,
     BR+, BL-, BR-, BL+,
     Effect: 1/1, 2/6, 3/2, 4/4, 5/5, 6/3
     Distorted orientations: TL/(-), TR/(-), BF/(+), BB/(+)
     Correct with:
     BB-, BL-,BF-,
     BB-, BL-,BF-,
     BB-, BL-, BF-
     BF-, BR-, BB-
     BF-, BR-, BB-
     BF-, BR-, BB-
     

These twists should be sufficient to bring a distorted skewb back into its initial state. If they don't, someone might have assembled the parts of your skewb in wrong order.

Enthusiasts will want to invent their own twists... just like I did. None of the combinations above has been taken from a book or web page, I have found them myself. Hint: The number of twists in useful combinations for corner turns or square exchanges can normally be divided by 3 or 4.

Here's one interesting combination which has been found by Kurt Endl, Professor of Mathematics and cube enthusiast (I must really get his book about the skewb one day):

Combination:

BF+, BR-, BF-, BR+,
BF+, BR-, BF-, BR+

Effect: BL/(+), BF/(-), BR/(-), BB/(+), centre squares are unaffected.