Grip Theory¶
This whole page is under construction
Grips¶
A grip is a thing you can turn. Every puzzle has a grip set.
On a 3x3x3, the grip set is \(\{ R, L, U, D, F, B \}\).
Twists¶
A twist has two things:
- A grip from the grip set, which we’ll call \(\gamma\) (“gamma”).
- A rearrangement of all the grips in the grip set, which has to keep \(\gamma\) in the same place.
For example, on a 3x3x3 the R' twist has the grip \(R\) and the permutation that cycles \(U \to F \to D \to B \to U\) and keeps \(R\) and \(L\) fixed.
Pieces¶
- A piece is a thing that moves around. On a 33, there are 27 pieces. Every puzzle has a piece set.
- Each piece has a grip signature, which is a subset of the puzzle’s grip set that determines which twists affect the piece.
For example, the grip signature of the RUF corner is \(\{ R, U, F \}\).
Surprisingly, a grip signature is the only thing we need in order to describe where a piece goes after a sequence of moves.
Applying twists¶
To apply a twist to a puzzle, take each piece that has the twist’s grip in its grip signature and change the grips in the grip signature according to the twist’s permutation.
For example, R' changes the grip signature of the \({U, R, F}\) corner to \({F, R, D}\). Now that corner will be affected by F, R, and D moves, but not U moves.
The rest of this page is under construction
Attitudes¶
Grip group from twists¶
Complex puzzles¶
Anti moves¶
Indistinguishable pieces¶
TODO: attitude sets
Blocked grips¶
To model bandaging, …
TODO
Jumbling¶
TODO: ouch