A master floppy cube?

I'm sure we're all familiar with Okamoto's floppy cube, as well as the super floppy cube later produced.

But does a fully functioning 4x4x1 floppy cube exist within the dimensions of the floppy cube (no 4x4x4 sticker mods)? I had a quick search and there wasn't anything that appeared.

On that note, is it even possible? I recall there being some discussion about the mass produced floppy being particularly innovative with its flexible pieces.

Because I've just been playing around with my 4x4x4 but rotating so that it functions as such.

And it's quite fun, and includes the switched edges parity error.

So has it been done and can it be done?

http://lmgtfy.com/?q=4x4x1

I feel my error was searching "master floppy cube" rather than "4x4x1"

But I am in awe.
Thank you

I believe olz has made the 4x4x1 as well as a 5x5x1.
Someone made a 9x9x1 also, I don't remember who.

EDIT: royal floppy cube