Configurations in a Rubik’s Square

Simon calculating how many configurations are possible in a Rubik’s Square – a flat puzzle he invented, resembling the Rubik’s Cube. He comes to the conclusion that there are only 384 configurations possible in a Rubik’s Square (including the rotations and reflections) and only 48 unique configurations. “For a Rubik’s Cube, it’s more or less 43.5 quintillion configurations!”

Think of a puzzle made of 9 wooden squares of some thickness. Every square (except the one in the middle) has one or two sides painted as shown below. The goal is to assemble the square to align the colors with on the edges. Flipping is allowed.

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