I designed a 4x4x4 soma cube in AutoCad and then built it with wood cubes. Now I want to know how many different solutions there are for it. Similar to the Bedlam Cube, there are twelve pentacube and one tetracube. Each piece is unique and if one is in the set and you can get a different piece by mirroring it, that one is also in the set.
You can look at the cube here: http://a360.co/29ZwWV7 (takes a while to load)
There is a 3D model view and you can also isolate each piece by right clicking on it. Exploded view of the wood pieces: https://i.imgur.com/jJkuYXd.jpg