The puzzles I am about to present here come from the idea posted on the twistypuzzles forum, beginning from this post. And I am sure someone did this before, I vaguely recall seeing this or something closely related on YouTube.
I bought sticlerless versions of The Unicorn and The Crazy Unicorn by mf8, but black versions will do as well. Here's The Unicorn with its moves (six faces, and four corners can rotate):
Here's The Crazy Unicorn, with the same moves available. Additionally it has circles on all of the faces. All the circles are stationary, they don't follow faces they belong to. Such faces with circles that don't turn are called "0" faces.
Under every center piece The Crazy Unicorn has an additional connecting piece that can change default "0" faces to "1" faces (the circle turns while the face turns). Below from left to right: A center cap, a connecting piece in "0" face orientation, and a connecting piece in "1" face orientation with two indentations facing up. The connecting pieces are orientated the same way the center cap is.
Both puzzles are compatible with one another. You can freely swap their faces (not only the layers, but actual single-colored faces). So I did exactly this. Below you can see yellow faces swapped. The yellow connecting piece followed the face it belongs to and is about to be inserted in the left hand side puzzle. Inside the other puzzle you can see other connecting pieces (red, green, and orange) that remained there.
So I swapped some faces, and flipped some connecting pieces, and as a result I have two new puzzles.
Puzzle 1: Four sides of the regular Unicorn, the white "1" face, and the yellow "0" face:
Puzzle 2: Two sides with no circles, blue, and green are now "1" faces, and red, and orange remained "0" faces:
There are many possible configurations. With The Crazy Unicorn alone, you can make eight Crazy Planets by simply flipping the connecting pieces. Adding plain faces of the regular Unicorn to the mix, makes a bunch of new possibilities.
If you're going to attempt making these modifications, you will need a masking tape, to hold the middle layers in place, a pair of tweezers to take out small pieces should they fall inside the puzzle, and a magnetic screwdriver, to take out tiny washers so they won't get lost (they are sometimes missing anyway).
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