Hi,

this is another batch of 3x3x3-variants.

Their common property is that they do not behave like bandaged puzzles.

For all of these variants one can give a subset of moves of the 3x3x3 which defines the possible moves of the variant.

Compared with this thread:

viewtopic.php?f=14&t=15016this time restrictions to halfturns are included.

The ten new variants are:

Bandaged 3x3x3: C000060 <U D L R2>

Bandaged 3x3x3: 18C000060 <U D2 L R2>

Bandaged 3x3x3: F7A00108 <U D2 L2>

Bandaged 3x3x3: 42000B5A00108 <U2 D2 L>

Bandaged 3x3x3: 202005AD <U F Fs2>

Bandaged 3x3x3: 42000000005AD <U F2 Fs>

Bandaged 3x3x3: 42000202005AD <U F2 Fs2>

Bandaged 3x3x3: 738005AD <U2 F Fs2>

Bandaged 3x3x3: C000C00 <L F Ls2 Fs2>

Bandaged 3x3x3: 18C600C00 <L F2 Ls2 Fs2>

Please note that the specially marked faces mean that the face is strongly connected to the core.

In total I identified 22 subgroups

which can be defined as subgroups of twistybility

which definition include halfturns

which can be implemented with traditional bandaging

which have at least two turnable adjacent sides.

Some (like the Quadromese cube) I already implemented years ago.

Some (like the Floppy Cube or the slim cube) are available als massproduced or 3D-printed puzzles.

3 subgroups are trivial because they are subgroups of the Floppy Cube.

The remaining ten were missing until now.