Polycubes
Polyonimoes are shapes made from squares. The pieces of the game Tetris are tetronimoes, each made from four squares. There seven possible tetronimos, shown below. Observe the green S and red Z tetronimos are mirror images.
Now, consider polyonimoes, solids built from cubes. Here's one built from five cubes:
https://upload.wikimedia.org/wikipedia/commons/thumb/c/cc/AGK-pentacube.png/240px-AGK-pentacube.png
Tetracubes are made from four cubes. How many possible tetracubes are there? Be careful to count mirror images separately.
The answer is 8.
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The seven tetronimoes shown in the figure can form five tetracubes, which have their cubes in the same plane. The S tetracube can be rotated in 3D to form the Z tetracube, and similarly the L and Γ tetracubes are equivalent.
The non-planar tetracubes can be generated with a base of three cubes in an L shape, and then placing the fourth cube on top of one of the cubes of this base. This gives three distinct tetracubes. Like the S and Z tetronimoes, two of these are mirror images that are not rotations of each other.