Soma Cube

A cube can be made from these seven coloured pieces. Can you work out the size of the cube?

Form a cube out of the seven coloured pieces.

Given a solution, how many different solutions can be obtained from rotating the cube? How many different solutions can be obtained from rotating pieces?

The Soma Cube is made from seven pieces. Each piece contains three or four units. In total the pieces have 27 units, which form a 3×3 cube. There are 240 possible solutions (not including rotations). Each solution has 24 rotations of the cube. Each solution has 96 rotations of the pieces. Every solution can be rotated so the T piece is in the bottom layer. If the T piece was in the centre layer, then it is impossible for the remaining pieces to fill all 8 corners of the cube.