[May 7, 2008: I use part of this process to finish up the cube now, but I do not get all the edges this way.] This is Part 3 in a series of posts to help you get to know the Rubik's Cube. If you really want to read all this, do yourself a favor and get a 3x3x3 Rubik's Cube first. Last time I checked they have them at Walmart, Target, and Kmart for less than $10. At Walmart in Oroville just before Christmas I saw them on sale for $5. Start with Part 1, which is the Vocabulary section. Study the actual cube as you read through it. Then do Part 2, which is the Edges section. Then when you are able to consistently get the edges come back to this section.
If the Edges get messed up while doing the Corners, you goofed. Fix the Edges and try again.
Conjugation A set of preliminary moves is done before the Corner Piece Series, then after the Series, these moves are undone. That way the Corner Piece Series can be applied to any three corners anywhere on the cube. Sometimes I get lost and can’t remember how to undo the preliminary moves. I end up having to fix edges. The better I get to know the Corners, though, the less this happens.
Corner Pieces Use the Corner Piece Series to move all but three corners Home. Rarely can three be moved into place at once. Don’t even think about it. Once in a great while you can move two pieces Home at once. Usually you can get one. Sometimes some pieces can not be moved Home without conjugation, or without moving them somewhere else first. At first, don’t worry so much about the Corners that are difficult. Work with the easy ones. Sometimes a Corner is in the right place, but not twisted (oriented) correctly. Move it away while moving another piece to its place. Then move the twisted one back into place in the correct orientation. I kept getting lost as I tried to take Corners Home at first. Make sure you turn the Cube so the trio of Corners that you are moving are situated with one on the Front of the Upper Layer and two on the Back of the Upper Layer. After you get good at putting one corner Home at a time, if you want, you can use conjugation to put two Home at once.
Once you are down to three remaining corners, use the Corner Piece Series one time with conjugation if necessary—and it usually is necessary—to place the last three corners in their Home Positions. Find a Corner Piece which may be moved along a cube edge and into place. If none can be found create one. Note the face color (of the second corner piece) which will come to the top face of the cube in a target position during a Corner Piece Series. Locate the third corner piece in the cube face of this same color and note the color of the third corner piece face which is in that cube face. Bring the third corner piece to the top of the cube, by various face turns, such that that color is in the top face of the cube. Perform the Corner Piece Series so that the target color of the second corner piece replaces this color. Reverse the preliminary face turns indicated above.