Polycubes

Geometry Level 4

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.

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