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Tripod Method

ostracod

Member
Joined
Nov 21, 2007
Messages
135
Location
USA
...A long time ago, I used my own method for solving the Rubik's cube, the Fridrus method (2x2x3 block, 2 edges, 3 c/e pairs, 5 piece LL).

Then Qqwref (Michael Gottlieb) gave me a lot of useful insight. He recommended that I use pure block building, and so I learned the Tripod method (2x2x2 block, 3 2x2x1 blocks, 1 c/e pair, 5 piece LL). (He also persuaded me to make my first block like a normal person... It was like I was living in a cave before!)


And so I worked and worked on this nice little method. I like it a lot, because you don't have to memorize many algorithms, and it relies more on intuitive thinking. The last layer (which contains 3 corner pieces and 2 edge pieces) can be solved in 2 steps with 6 memorized algorithms.

You can see the method specifics on my site:

http://web.mac.com/teisenmann/Tripod/main.html


Recently, I have been wondering what the essential differences between the Tripod method and Fridrich method are. The cross and first 3 c/e pairs can be used in both the Fridrich method and Tripod method for the first few steps (although I like block building better!). After the cross and 3 c/e pairs, the methods differ:

With Fridrich, you solve the last c/e pair, then solve the 8 pieces in the last layer using algorithms.

With Tripod, you solve a 2x2x1 block in the last layer, THEN the last c/e pair, and finally the 5 remaining pieces w/ algorithms.


...So now I have a couple questions.

If you want to memorize a SMALL number of algorithms, is it faster to use the Tripod method? In other words, is intuitively solving a block faster than algorithmically solving the entire LL? (Keep in mind that solving the last c/e pair in Tripod is more restricted.)

And alternatively, if you want to memorize a LARGE number of algorithms, is Fridrich faster? A 1 step LL in Tripod and 2 step LL in Fridrich require about the same amount of memorization (I haven't found the actual amount, because I don't want to memorize a lot! :P)

Comments are welcome!
 
If you have the case which you have given, you first do R' F R F'. Then you have one of the first cases listed on my site. You could either re-orient the cube and solve the case using the same mini algorithm, or you could re-orient the algorithm, and do F' U F U'. Now you have your corner edge pair. Lastly, you do F R' F' R to put it into place.

It's important to note that the mini algorithm can be done very fast with finger tricks... In about half a second! R' F is done with one hand motion (right wrist turns down and index finger turns F), then as R moves back up, the left index finger pushes F back as well.
 
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Ah yes, that works. I think it would be good to have the cases grouped precisely by number of Frifris, i.e., first all cases with 1, then all with 2, etc. And I'm not convinced all cases are covered. Are they?
 
The cases actually are already grouped by number of Frifris, in the way you described... Except not counting the c/e pair placement, which I suppose would be useful.

I'm fairly certain that all cases are listed (mirror cases are not included). If you think a case is missing, tell me.
 
I didn't have a missing case, it was just not clear to me that all cases are covered. After thinking/checking a bit, I think you got all. Though I still think it would be nice to have that proven on the page, at least somewhat.

This picture is wrong, btw:
http://web.mac.com/teisenmann/Tripod/main_files/9__$!%40!__pastedGraphic.png

And yes, the pair placement placements would be nice to have, too.
 
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Whoooops! Didn't see that, thanks. I'll consider adding a c/e pair case section. It takes 1 or 2 Frifris to place the corner edge pair, depending on the case.
 
I'm not sure if anyone's following this thread anymore... But I think I found a way to eliminate half of the tripod last layer permutations.

Normally there are 5 pieces in the tripod last layer, with a little over 100 possible permutations. But when placing the last c/e pair, it is possible to orient the edges by adding a few more moves. With this technique, there would only be 50 permutations, and half as many algorithms to memorize as before! I think I'll try using this trick for a while to see if it is helpful.

...If anyone is curious to know how to orient the edges for the LL, just ask.
 
"Use the mini algorithm "Frifri" to solve a corner edge pair in the tripod. Frifri is simply R'F R F'."

That seems pretty clear to me... Frifri is the name of a mini algorithm, which is R'F R F'.

When you have a Tripod of unsolved pieces, Frifri is the ONLY move you can do without messing up everything... without using algorithms (or commutators). The key to using Frifri is learning the cases in which it pairs a corner and an edge together.

Alternatively, you could solve the Tripod using only algorithms, but that defeats the purpose of having a small number of algorithms to memorize.
 
I never thought of the name like that before. :O But yes, I guess it would make sense to call it that. The origin of the name "Frifri" came from the Fridrus method, and is just a repetition of "Fri".

I'm making a table right now to find out how many algorithms one would need to memorize for a 1 step "nicer" last layer. I'm excluding cases in which commutators can be used...
 
Yes, I've greatly appreciated that source since I found it a while back (Thankyou Jessica Fridrich!!). The only problem that I find is that all of the algorithms are given as if the last layer were on the F side (I assume she holds it higher so the front is closer to her face?), so I have to reorient them for a U side LL. But it's convenient to have all the "nice" last layer algorithms in one place.

With edges oriented in this kind of last layer, one has to memorize only 17 algorithms if he/she knows how to do commutators and a corner twisting technique. The solver will then be able to solve the last layer in 1 algorithm. I am definitely going for this!... After the craziness in school theatre is over though. >_>

James, I'm interested in how your approach works. Is it somewhat like the Heise method, where you place all edges and 2 corners, then solve the rest w/ commutators? Or something different?
 
It really varies, mostly I would pair up a corner and an edge in 1-3 moves then place it while putting whatever I disturbed back, leaving either 2 misoriented corners or a solved cube. It was really just conjugates.
 
You do this when there are 5 unsolved pieces left? How do you join pieces without destroying other things?? ¿_? I thought Frifri was the limit of c/e pair creation/placement, because one can do R' F R F' without disrupting solved parts of the cube. I would really like an example!
 
I hope this hasn't been discussed before, but I glanced through the site and posts and didn't see anything. What is the average move count you are getting with this method?
 
I haven't done a precise move count lately, but I find it has a low move count (block building tends to be very efficient). Perhaps Frifri adds a few extra moves, but if one could learn a 1 step last layer (w/o edges already oriented), the move count would be very low. I'd say it's comparable to the Petrus method in moves, maybe a bit more to be conservative.
 
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