EDIT: Oskar has already used the name "Floppy 2x2x3"!! So I changed the name at the suggestion of Joshua Bell. Everything should be all right now.

The Loppy 2x2x3 is my first-ever mod, and has a special first-mod quality. And that means that I literally made it at 10 pm with the things laying around at my desk. If anyone expresses interest in buying it, I will improve it for you (e.g. getting real stickers, replacing the little eraser bits with actual plastic, etc.).

What it is
It's a mass-produced 2x2x4 with one side removed. Therefore, it is a 2x2x3 that can change shape. Solving it is mostly like solving the 2x2x4, but a bit simpler.

Pictures and Video
The video is located here

Here it is solved. You can see the true, awful nature of the white stickers (paper labels supported by little cubes made of eraser material).

This is what one quarter-turn looks like.

Here it is after one shapechanging half-turn and a few non-shapechanging turns.

Selling it
If you want it, it's available. There are two options:
- If one person is willing to pay over $45 for it, I'll wait a week (to make sure nobody else wants it). Then I'll sell it to you, probably through eBay.
- If two or more people are willing to pay over $30 for it, then I'll put it in a 3-day eBay auction.

What I said before still applies: before I sell it, I'll fix it up nicely. It won't have brand-new stickers, but it also won't have stickers made of old paper labeling stuff, so there's that.

Can we have a photo of this? I'd love to see your work.

This is not the same puzzle as Oskar's (based on a 3x3x3) so perhaps you should change the name.
How did you independently come up with the same name, by the way?

But please do put up some pictures, they're quite essential for presenting a new puzzle.

Kudos on diving in to mods so quickly, and don't feel bad about either the name collision or the rough nature of your first mod. I just got my collection out of storage and while I'm impressed with how well I did the 2x3x3 the 2x2x4 is pretty embarrassing... to the point I'm thinking of redoing it, even though they're now mass-produced. Sadly, the 2x2x3 went AWOL...

(And lets not even talk about the "faux" 3x3x5 which was merely extra cubies glued on to two ends... at one point we thought that was cool!)

As far as a name, how about "Loppy 2x2x3" as it's "lopsided"?

"Floppy" derives from Okamoto's Floppy Cube, where the corners connect diagonally to the core via a foot hidden under a flexible (i.e. floppy) piece of plastic. Okamoto's "Super Floppy" is capable of 90-degree turns, but dispenses with the flexible plastic so the minimal cut-outs for the feet can be seen. Oskar's Floppy 2x2x3 and 2x3x3 extend this notion and can be seen as logical extensions of the Super Floppy, if it were considered middle layer of a 3x3x3. Hence, they're reasonable uses of the name, even though "Floppy" no longer strictly applies. "Floppy" is now also used as a generic term for 1xNxN cuboids in honor of Okamoto's pioneering work, just as "Domino" is used for 2xNxN despite most such cuboids having traditional stickers. So... "Floppy" has two commonly accepted uses, and should be avoided for this.

Other "lopsided" cubes have been made before; my 2x3x5 was temporarily a "lopsided" 2x3x4 when I'd only extended one side. 3x3xNs that are made via extensions of crazy/super 3x3x(N-2)'s can be halfway extended, and some are mass produced. All that said, I don't recall a lopsided 2x2x3 being shown before so please do share!

Thank you everyone for your interest, and I now have pictures up. Yes, it does exist

And thank you Joshua for the name "Loppy ("Lopsided") 2x2x3". It makes sense so I'm using it.

From all the talk of "floppy", I thought it meant a puzzle that changes shape because it's actually a larger puzzle with some sides deleted (like Oskar's Floppy 2x2x2). This is a 2x2x3 that changes shape because it's really a 2x2x4 with one side deleted, so the "floppy" name made sense (to me).