A Little Chop with two additional restrictions which transform the puzzle into the equivalent of the M24 Group, one of the sporadic groups.

• Inventor: Casey Mihaloew
• Mechanism: Constraints without bandaging
• Patents: Unknown
• Producer: 3D printing service
• Year: 2020
• Original Price: $0.00 USD
• Current Price: No Data

This puzzle appears to be a 24-cube or Little Chop. Indeed it allows the turns of that puzzle but it has two additional restrictions which transforms it into the mechanical equivalent of M24, which is one of the 26 sporadic groups.
The puzzle has two restrictions:
1. Moves must alternate between clockwise and counter-clockwise. This has no effect on the puzzle and is just a consequence of the design of the mechanism.
2. Once you made a turn, the next one has to be on an edge that points in the same direction, or in other words, is parallel.

The mechanism is probably simpler that one would expect. It uses a similar technique to the Alternating Cube (see the separate entry) and the Alternating Asynchronous Antislice Face Turning Octahedron (see the separate entry) from the same inventor. The basic idea is that there are toggles on the inside that are driven by some subset of the axes. There are four toggles in this one, one driven by all axes and one for each pair of axes that point in the same direction. The three pair toggles are one one layer and the full toggle is on a layer by itself. Image 3 shows the core of the puzzle with one for the pair toggles in it alongside the pair toggle by itself. Image 4 shows the assembled mechanism alongside the two types of axes showing how the drive the toggles.
The reason this works is that each toggle in its initial position only allows clockwise turns, but those swap them into a state that only allows counter clockwise turns afterwards, which then put it back in the original state. A single turn swaps the full toggle and a pair toggle, so either that turn or the other turn pointing in the same direction can be moved counter-clockwise next. For the other four axes, the full toggle forces them to only turn counter-clockwise while their pair toggle forces them to turn clockwise, so they can't move either direction. Partial turns block any other axis from turning, so jumbling turns aren't possible.

Not surprisingly, there are a lot of neat properties of the positions of this puzzle. The unrestricted (super) 24-cube has 24!/2 = 310,224,200,866,619,719,680,000 positions while this puzzle has only 244,823,040. If you ignore rotations and recolourings, these numbers become 4,509,264,634,875 and 5,100,480. There are only 2 solved positions of this puzzle: the original colour scheme and its reflected image. There are a lot of different colouring schemes of this puzzle that show off different properties of this group. For example a 3-colouring with a colour for each direction a long edge of a piece can point that gives the trio subgroup, and show a 6-colouring (a refinement of the 3-colouring that alternates 2 colours for each of the original 3 colours) that gives the sextet subgroup. The other maximal subgroups also have stickerings that give them, although the point subgroup is boring and the projective line subgroup is very confusing.

The shape is the Steinmetz solid, a combination of three cylinders.
It was printed using i.Materialize and stickered with machine cut stickers.
Diameter (of cylinder): 64 mm
Weight: 113 grams

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