Intuitive Tripod

In my Discord server, Ryan Hudgens (OreKehStrah) once suggested the idea of doing something with Megaminx Tripod LSLL involving taking advantage of the rotational symmetry. I decided to start looking into this, using a 3x3 instead, and had the idea of creating three pairs then solving from there. Typically the solve will end in one of the following triggers. The last four triggers are the same as the first two triggers if an x y or z' y' rotation is used, which could be used for some who want to simplify the thinking. Each trigger in the list has a note next to it. Parentheses means those two pieces swap and a + or - means that the piece at that position will be clockwise or counter clockwise twisted upon performing the trigger.

• U' R U R': (UFR- UBR) (UFL- DFR-)

• R U' R' U: (UFR UBR+) (UFL+ DFR+)

• F' U F U': (UFR UFL-) (UBR- DFR-)

• U F' U' F: (UFR+ UFL) (UBR+ DFR+)

• R' F R F': (UFR+ DFR+) (UFL- UBR-)

• F R' F' R: (UFR- DFR-) (UFL+ UBR+)

A note on Tripod rotations: In Zbigniew Zborowski's document for the C2GR method, a CEOR like method, he uses the letter "a" for diagonal axis rotations. In this case, a would be equal to x y and a' would be z' y'.

Observation: Using only these triggers to scramble the cube appears to result in a special Tripod corner orbit. It seems necessary to prepare the corners first to permute them into the Tripod orbit in order to allow for ending the solve using only the triggers. For example, the scramble R' F R F' is obviously solvable using the inverse of that trigger (F R' F' R). But if two corners are swapped after applying that trigger, as in R' F R F' U' L U' R U2 L' U L U2 L' R' U2, the corners can't be solved using any combination of the triggers. So Tripod corner orbit placement needs to be done during inspection using CPFB or similar, before or during solving the final 1x2x2 block, immediately after solving the final 1x2x2 block, or during the pair building step. Or simply build pairs without worrying about this orbit and finish the solve after forming the pairs using the triggers or other moves for the special cases. To determine if the corners are in the correct orbit, check if the corner swaps match any within the trigger list. If not, a corner swap is necessary.

Intuitive corner solving: the UR based triggers swap the UR corners an the other two corners, FR triggers swap FR, and FU triggers swap FU. It appears possible in Roux, 42, WaterRoux, Corners First, or other related methods to locate the swapped corner pattern and do a cube rotation to put the adjacent swapped corners at UR to always allow for solving and thinking only in the U' R U R' and R U' R' U triggers. Another possibility is to place the solved/oriented/tripod corner from UBL at UBR and do R U R', r U r', R U' R', or r U' r' to place the corners into the Tripod orbit. Or place the corner at UFL and use the U and F equivalent moves. This would allow for completely intuitively solving CMLL in Roux or L5C in 42. It would also be better for those who don't want to learn a lot or for beginners. So a good beginner progression in the Tripod method may be to start out solving the corners then using commutators for the last three edges. Then they can progress to forming pairs.

Pair making observations: When a pair is formed, the other corner from that bar that includes the edge (UR, FU, or FR) must be paired with a different edge. When a pair is formed using UFR, the other corner from that bar that includes the edge can't be used after that point.

Temporary pseudo alignment: Moves like R' F x, F R' x, U' R y, R U' y, U F' z, and F' U z perform half of a trigger to create the tripod shape in another location. This may allow for easier manipulation in some cases where the pseudo tripod is created, a trigger or few are performed in the new tripod location, then the pseudo tripod is undone.

Current problem:

Scramble: R' F R F' R U' R' U R U' R' U U F' U' F

The inverse is the optimal trigger based solution. But if someone does R' F R F' R' F R F' F' U F U', it leads to just two pairs solved and two corners needing to be twisted before applying  a final trigger. This is a bad situation that requires many moves to solve. How should pieces be influenced during the formation of the first pair in order to lead to a final trigger or two that forms the last two pairs?

If not placing the corners into the Tripod orbit: In the Tripod method, after the three pairs are formed, use a final trigger to solve the pairs as close as possible, leading to a two pair swap situation. Then use L' U2 R (U/U') R' U2 R L, plus a possible pre-rotation of a or a', to 3 cycle two of the pairs and one pair from one of the 1x2x2s. Then use a pair 3 cycle again to finish. Or learn an alg for the three pair formed situations when two pairs are swapped, instead of doing any pair placement triggers first.

Below are the finishing pair combinations:

• R' F R F': UFr, URb, dFR 

• R U' R' U: UFr, URb, dFR 

• F R' F' R: UFl, URf, dFR 

• F' U F U': UFl, URf, dFR 

• U' R U R': UFl, URb, uFR 

• U F' U' F: UFl, URb, uFR 

• Simplifying the above, in order to have a trigger ending, a pair must always use UFR.

• The three pairs at UFl, URb, and dFR, not using UFR, can be done, but must be solved using a 3-cycle (L' U2 R U/U' R' U2 R L) with a pre move before it such as l', b, or similar. Or maybe R U, then L' d L U L' d' L U2 R' or a translated version of that.

In 2010, Gilles Roux posted a thread to SpeedSolving.com showing an observation that he had made. He noticed that using these special trigger commutators always results in corners permuted or in special configurations. There was no method or proposed use in the thread, but I was reminded of this thread as I started working on the ideas that I presented on this page.