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What if instead of gluing squares together at the sides you glued them at the corners, but ensuring that the side of one square is always at right angles to that of any contiguous square? Since a square has the same number of corners as it has sides, 4, does it follow that in the case of 5 such squares for example, there are 12 possible arrangements, just as in the case of pentominoes?

What about cubes? Since a cube has more sides (6) than corners (4), are there then more such side gluing than corner gluing arrangements?

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