Hello everyone.
I searched the forum and it turns out that we don't have definition for mixup puzzles (or I failed to find one). Any other kinds have their own strict definitions (doctrinaire, jumbling etc.), so I thought mixups also need one. Here's my attempt.

Firstly, let's define two things.
By layer or slice I mean group of pieces that move together while rotating by given axis. This one is obvious, ex. FULRBDMES in Rubik's Cube.

Second definition: atomic twist - the shortest twist after which other moves are possible [source]

Now, my idea is something like this:
Mixup puzzle - puzzle where layers on the same axis have different atomic number.

Let's take 3x3x3 cube and Mixup Cube.
Both have 3 layers per axis. But in case of 3x3x3 each one have atomic number 90° when on Mixup Cube middle layer has 45°.
That definition would work but the problem is that the Doctor Skewb has only one layer per axis (it's slice only mixup master skewb). So one needs to find better one or makes above one more precise. Any ideas?

Krystian

Another good example for a puzzle with "mixup" property is the Hexed mixup.

If would prefer to define "mixup moves". The doctor skewb then is a puzzle consisting only of mixup moves. The Mixup cube is then a hybrid puzzle. See the Equator in the museum. That is a puzzle comparable to the mixup cube but without traditional moves. It seems strange to define a hybrid puzzle as normal and the reduced puzzle as abberation.

Andreas

So am I right in thinking that mixup moves are just a variation of shape-changing?

No... a Mixup Cube could be in the shape of a Rhombicuboctahedron and then it wouldn't change Shape. The only shape I'm sure would work for my Doctor Skewb would be a Sphere.

As for a definition of Mixup... I'm thinking of it as an adjective that can be applied to an already existing puzzle. A Mixup Cube or Mixup 3x3x3 takes a normal 3x3x3 and allows 2 normally seperate piece types to be interchanged (aka mixed up)... in that case the edges and face centers can be interchanged. In the case of my Doctor Skewb its a Slice-turn-only Mixup Master Skewb. It takes a Master Skewb and allows the edges and the X-faces to be interchanged. The Slice-turn-only adjective is then applied to that puzzle.

Carl