Rectangles Constructed with Tetrabolos

All possible rectangles are shown here, but the impossible ones are more interesting. Due to the small number of pieces you can enumerate all cases and prove the other rectangles impossible to build, but this isn't a preferable method.
Rectangles built of all tetrabolos can't be constructed, because there is an odd number of odd pieces and the argument goes as for hexabolos . To prove the 3s x 8s and 4s x 6s rectangles to be impossible is much more difficult.
Nice convex shapes using all tetrabolos are shown by Michael Keller.
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