Howdy all,
Here are some pictures and details of the 2x2x1 that I recently printed. Of course plenty of others have made a 2x2x1, including a
4-piece 2x2x1. My original idea was for a 4-piece 2x2x1 that didn't rely on the flexibility of the material for assembly. After I drew it up, it was painfully obvious that the mechanism would be blocked after 1 or 2 twists.

I fixed that by modifying it into a 5-piece design and decided to print it anyway.
It is held together by a single M3 screw. The screws I already had were too long, but I found that it's easy to cut M3's with moderate-size wire cutters. This puzzle actually still needed a bit of flexure to assemble, because the puzzle was not built to have a 1.8mm screwdriver wedged between the pieces.
The interlocking bits of the puzzle were designed with 0.2mm clearances, which worked great. For the M3 screw I used a 3.25mm clearance-fit hole and 2.75mm interference-fit hole. The wall thicknesses are all 2mm thick (plus or minus the 0.2mm clearnce), which is very sturdy. The cubies are 19mm on a side. I made the computer model with OpenSCAD.
I printed it in Shapeways polished Purple, strong, and flexible. The Shapeways polishing process mainly removes the loose, grainy stuff on the surface of the unpolished pieces, so I decided to sand the pieces further (I had also planned to fillet the pieces by hand all along). Then I discovered that the pieces were white in the bulk with purple dye. The picture below shows three pieces sanded and one plus the internal piece in their as-received condition. Shapeways' colored nylon SLS
looks great, you just can't sand them without sanding away the dye.
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2x2x1 - Sanding.jpg [ 105.37 KiB | Viewed 521 times ]
So I had to paint them. This went quite well. I sanded the paint very lightly afterwards, and that improved the smoothness a lot.
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2x2x1 - Painted.jpg [ 106.6 KiB | Viewed 521 times ]
I stickered it with a 2-color scheme. There are two 2x1 faces and one 2x2 face with each color. This makes each of the 4 pieces distinct. I originally planned to only sticker the 2x2 faces, but that would make some of the states look the same. With only 6 permutations in the first place, I didn't want this puzzle to get any easier!

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2x2x1 - Finished 1.jpg [ 78.1 KiB | Viewed 521 times ]
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2x2x1 - Finished 2.jpg [ 78.4 KiB | Viewed 521 times ]
The sticker pattern looks great because it helps the puzzle look more scrambled that it is, especially to someone who's unacquainted with twisty puzzles and hasn't been taught to "see the pieces, not the stickers."
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2x2x1 - Scramble.jpg [ 83.56 KiB | Viewed 521 times ]
I picked these colors because I made this puzzle as a gift for a girl who's a big football fan of her alma mater, the Louisiana State University Fighting Tigers!

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LSU Tigers Logo.jpg [ 55.14 KiB | Viewed 521 times ]