Monday, January 4, 2010

Corner Piece Series

This is a series of turns which will move 3 corners on the upper face either clockwise or anticlockwise. This graphic, from the original site, is quite helpful, and is looking down on the top face.



Were this in traditional notation, it would read U R U' L' U R' U' L

This video shows what will happen when this Corner Piece Series (CPS) is applied to a solved cube. 




We notice that
  • the upper front right corner has not moved
  • the upper back right corner has moved along the back edge and in the process, has rolled over
  • the upper back left corner has moved along the left edge and in the process, has rolled over
  • the upper front left corner has moved diagonally across the top face, and in the process has rolled over so that the left colour of the corner (orange) has ended up on the top face of the cube
  • the first turn of the upper face was clockwise (or to the right)
  • the 3 corner pieces moved anticlockwise around the top face
  • the second turn was a turn of the right face away from you
Now let's follow the same kind of sequence, but this time begin by turning the upper face anticlockwise.



This sequence would be U' L' U R U' L U R'.

This video shows what happens:



This time, we notice that
  • the upper front left corner has not moved
  • the upper back left corner has moved along the back edge and in the process, has rolled over
  • the upper back right corner has moved along the right edge and in the process, has rolled over
  • the upper front right corner has moved diagonally across the top face, and in the process has rolled over so that the right colour of the corner (red) has ended up on the top face of the cube
  • the first turn of the upper face was anticlockwise (or to the left)
  • the 3 corner pieces moved clockwise around the top face
  • the second turn was a turn of the left face away from you

We can now summarise the Corner Piece Series.
  1. Three corners on the upper face will move in order about a triangle on the top face
  2. If the first upper face turn is clockwise
    • the corners move anticlockwise
    • the upper front right corner doesn't move
  3. If the first upper face turn is anticlockwise
    • the corners move clockwise
    • the upper front left corner doesn't move

Here's a beginner's video explaining exactly what's going on.



And finally, for the curious, here's a video showing how the Corner Piece Series may be used on many different puzzles.





At this point, we've seen the only two series of moves needed to solve the cube. The EPS will move 3 edge pieces around the upper front right corner. The CPS will move 3 corners around the upper face.


Let's start solving a scrambled cube.

17 comments:

  1. Is there a picture of a CPS that starts anticlockwise?

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  2. @zachary,

    There wasn't one on the original site. I've just made a very rough picture which is now on this page. It's not pretty but it shows you what you need to know.

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  3. I don't see the animations. Are they still up or am I missing a program I need installed?

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    1. The animations work. I've tested it firefox, chrome and internet explorer. I suspect your browser is just missing some kind of java plugin.

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    2. Latest java update 7v51 dislikes the lack of manifest for the applets. Until 45 they still worked but warned of removal in a future update, that update from 7u45 to 7u51 stops your applets.

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  4. Hi Chareaves,

    I'm doing the Rubik Siamese cube (also call fused or double cube),
    im using the ultimate solution, and almost solve it, i handle the edge pieces fine, no specific algorithm and no memorize at all.
    I have a problem with the corner piece series, the only moves i can do is R and U (and M), its been a few long days to try to figure how i do a corner series in this cube, there is some algorithm i found in YouTube, but i want to solved it and not just memorized it.

    can you help ? any idea how to switch corners ?

    Thanks

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    1. Hi aviron

      First thing, I don't have one. So these thoughts will be just thoughts.

      If you do (U'RUR')x3, that will swap the UFL and UBR corners, as well as swapping the UFR and DFR corners.

      That should enable you to at least place the corners. (This is assuming you don't have parity issues on this puzzle where you end up having to swap two corners).

      To orient the placed corners, I'm not sure without having the puzzle. Perhaps I'll buy one!

      Let me know whether you can place them all.

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    2. Thanks, its real help, still working on it, but its a good lead,
      I will try to placed them all, no parity issue should be with this puzzle.
      I recommend this puzzle, very challenging to solve it with no specific algorithm.
      you can found one in Calvin site (i see you already solve the ultimate cube).

      I will let you know how it goes.

      Thanks !

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    3. Actually I couldn't find it on calvin's site. Can you point me in the right direction?

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  5. For no reason i already knew this algorithm to the bones, although i don't ever use it in my method. Also it always been my favorite, it can't be a coincidence :D, i'm very happy to see i have to use it now.
    I'm max interested in intuitive ways to solve the cube, i'm done with the basics so here i go, wish me luck. :)

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    1. Hi Pablo

      Excellent! I think the corner piece series is one of a number of variants of commutators. It just happens to be the one Phil Marshall chose to use, I think as the pieces are on the top face and it's all very symmetrical and easy to remember.

      There are heaps of puzzles on this site and the methods are as intuitive as possible, using the CPS and EPS. Good luck!

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  6. Thnk you so much for your web site, I'm looking forward to using this method! I'm having some troubles with the java code on the site though, so it's pretty hard to tell what to do. I have the latest java installed and have tried with IE, Firefox and Chrome with the same results. The java app areas show the java animation then come up with a red x that says "error click for details" clicking that says that the AnimCube.class object was not found. Any help would be appreciated!

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    1. Hi Ron
      Thanks for your comment. I know exactly what's happened, and wouldn't have seen it if you hadn't commented! The animations are housed on a website which no longer exists. Hmmm. I'll have to have a think about this because I'm not sure I can get the animations back. Worst case I'll have to delete the bits with animations. Honestly, the final video on this page (Corner Piece Series Explained) is really all you'll need.

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    2. Back again. I think it's fixed! I moved the code to a different url. Try it now. It all works well on my machine (chrome). Please let me know whether you can see it now.

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  7. Hi,
    I am using Chrome, and your final video does not appear at all. It is just a blank space in the blog. Just an FYI, in case a link broke.

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    Replies
    1. Hmmm. Thanks. I'm using chrome now replying to this and the video is definitely there and playing. perhaps there's something else going on at your end. All seems good here.

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