In this tutorial I'm going to show you how to make a Rubik's Cube, which changes the shape when you scramble it.

The cuboid is easy to make, because you don't have to extend any pieces.

Check out step 5 to see, how to solve it. Basically it solves like the 3x3x3, so if you know how to solve that one, you should have no problems. A big advantage compared e.g. to the Fisher Cube is, that there is no parity.

Also you can easily shove it into your pocket because it is a lot thinner than the original cube.

Step 1: What You Need

This is what you need:

material:

A black Rubik's Cube (Best is a DIY Cube, because you can easily assemble and disassemble it. Also it comes with a set of stickers, which you can later use). You can of course use an assembled cube, but you will have to get rid of the stickers, before you start.
self-hardening synthetic clay (I used “Apoxie® Sculpt”)
Tiles or stickers (e.g. from cubesmith.com). Just get the regular 3x3x3 sized ones. Tiles are better, because they can compensate small irregularities.

tools:

a Dremel (Felt Polishing Wheel, SpeedClic Plastic Cutting Wheel) if you don't have a Dremel, just use a regular saw
sandpaper (400, 800, 1000)
a black permanent marker
a box cutter

Step 2: Cut the Pieces

First mark the lines as shown in the first picture

Now cut down along the lines. I used the SpeedClic Plastic Cutting Wheel from Dremel, even though it is not long enough to cut through all the pieces. The heat melts the pieces together (you can easily undo it with a box cutter) like this they cannot get out of place (remember to let the Dremel cool off in between).

If you are using a saw, it is probably a good idea to hold the pieces in place with some tape, or to disassemble the cube and mark the lines on every piece. You can also use a rasp or a belt sander. So just choose whatever works best for you.

If you don't know how to disassemble a cube watch Dan Brown's video on how to cheat:

Step 3: Grinding

Before filling the cube you will have to disassemble it. Then fill the pieces with the self-hardening clay as shown in the first picture.

If you are using a DIY Cube you should leave holes to adjust the screws, as you can see in the second picture.

Apoxie Sculpt is completely dried after 24 hours, you should wait to get a perfect result.
Now grind every single piece so that you are able to reassemble the cuboid.
Assemble it and grind every side (start with the sandpaper with the lowest number). Remember to sometimes turn one layer of the cube, to do it equally.

I work pretty messy, so nearly always I have to apply a second layer of modeling clay, to smooth out the holes. Afterwards I grind the cube again to get a perfect result.

Step 4: Paint the Pieces and Cut the Stickers

Paint the pieces with a black permanent marker. You don't have to paint them entirely, because the stickers will cover the faces. Use the Felt Polishing Wheel to get rid of the extra colour, else it will later stain your fingers

If you're done, reassemble the cuboid and cut the stickers, so that they will fit on the pieces of the top and bottom layer. For the sides I used regular ones because I was to lazy to cut every single one and as you can see in the pictures it still looks good.

Congratulations, you are done!

Step 5: Solve the Cuboid

Dan Brown made two very good videos on how to solve the cube, check them out to find out how to generally solve a Rubik's Cube. In order to solve the cuboid you just made (you should know how to solve the 3x3x3) take a look at the pictures... Or try to figure it out yourself, it is not that hard...

LIST OF ALGORITHMS
1) Fi U Li Ui
2) Ri Di R D
3) U R Ui Ri Ui Fi U F
4) Ui Li U L U F Ui Fi
5) F R U Ri Ui Fi
6) R U Ri U R U U Ri
7) U R Ui Li U Ri Ui L
8) Ri Di R D

And the second part:

There is also a good instructable on this subject, check it out:
www.instructables.com/id/How-To-Solve-A-Rubik-s-Cube!/

Step 6: What Now?

There are many ways to modify not only the shape of the cube but also the mechanism.

So get creative and build your own cube.

These sites might help you:
Good article on what tools and materials to use:
tonyfisherpuzzles.net/F%20Puzzle%20Making%20Tools%20and%20Materials.html

Many cubes and explanations how to make them:
http://www.speedcubing.com/ton/Building.htm
www.cubemania.co.kr/bbs/zboard.php (in order to see the explanations, you need to log in)