I had several tiles left over from my chess set, and was pondering what to do with them. I decided to try making a checkered LEGO Soma cube. LEGO bricks have the wonderful property that 2 studs is exactly the same length as 5 plates height. I decided to double this, making each of the 27 smaller cubes measure 4 studs on a side. I connected the cubes together internally, giving no evidence on the outside.
After completing the first cube I decided to try making a smaller one. Since each of the component cubes measured 2 studs on a side, there would be no room to put hidden bricks on the inside. I figured that by using 2 x 2 corner bricks, I could connect any place where 3 cubes came together at a right angle. All the pieces in the Soma cube could be oriented in a way to make this possible except the large 'L'. For this piece I used both the corner bricks and 1 x 2 technic bricks with 2 holes. Here is the piece with the top tiles removed to see the internal structure. As it happens this second strategy would work for every piece without the corner pieces, except for the 'Y' piece, which requires the corner brick.
The smaller cube has the same color pattern as the larger one except for the large 'L' which is inversed. Both cubes are solvable with a chequered pattern. The large cube has 219 solutions, while the smaller cube has only 21, making it much more difficult. The larger cube is built to have a solution with all studs oriented the same way; the smaller cube can be solved such that all faces are smooth (no undersides of bricks visible.)
Hey, that's the second Soma Cube I found today which is built the same way as I built mine in LDD a few months ago :-)). I just built mine with white corner cubes instead of black ones. If you like, check my page to compare them: http://www.mocpages.com/moc.php/287614