Square-1

[SparkZer00]

I already know how to solve the square-1, and am trying to get faster. In solving, I have been noticing that my method I use to square the puzzle is quite inefficient. What I do, is I pair all the edges together in the top layer in either ceceeeeeee or cceeeeeeee and solve using the patterns on jaap's puzzle page. Seeing as this takes 10 seconds to do at least, I have been looking for a new method to get the square-1 into the cube shaped. Here's where my problem is: I looked on Lars V.'s site and his "Getting it into the cube shape" page doesn't seem to have anything regarding actually squaring the puzzle, it's just an analysis of the shapes a layer can have. He did mention on that page that there is a squaring method that takes 7 twists at most, and I haven't been able to find that method. Can someone help me? I've been looking for a while now, but I feel I've just been stumbling around in the dark.

Thanks

 

[PatrickJameson]

http://www.geocities.com/jaapsch/puzzles/square1.htm#s1

For a simple cube shape solution. Or...

http://www.geocities.com/jaapsch/puzzles/square1d.htm

 

[SparkZer00]

The first link was the Jaap's puzzle page i was originally referring too

I have already seen the chart on the second link, but I have had lots of cases not shown there or the top and bottom are flipped.

 

[cuBerBruce]

Jaap's diagram shows all the possible shapes (65) up to symmetry of swapping top and bottom, and reflections. If the diagram has top and bottom shapes reversed from what you have, just turn the puzzle over (or turn the diagram upside down). If the shape you have still isn't in the diagram, then its mirror image will be (possibly upside down).

 

[Kenneth]

I created an article about Square-1 in the wiki. There is also a page about Square-1 speedsolving methods but it is not much there yet. If someone can make the images? (not stolen from a page without asking for permission) then I can help putting up a wiki-page with diagrams that shows all combinations.

 

[SparkZer00]

Jaap's diagram shows all the possible shapes (65) up to symmetry of swapping top and bottom, and reflections. If the diagram has top and bottom shapes reversed from what you have, just turn the puzzle over (or turn the diagram upside down). If the shape you have still isn't in the diagram, then its mirror image will be (possibly upside down).

but wouldn't flipping over the puzzle misalign you if you go to execute an algorithm?

there are also the shape possibilities that aren't on that chart

 

[Mike Hughey]

Jaap's diagram shows all the possible shapes (65) up to symmetry of swapping top and bottom, and reflections. If the diagram has top and bottom shapes reversed from what you have, just turn the puzzle over (or turn the diagram upside down). If the shape you have still isn't in the diagram, then its mirror image will be (possibly upside down).

but wouldn't flipping over the puzzle misalign you if you go to execute an algorithm?

But you're not executing an algorithm. You're just going to the next state in the chart. Just align the two faces the proper way and then do a slice move. That should work just as well with the puzzle upside down, right?

there are also the shape possibilities that aren't on that chart

I'm sorry - I haven't ever really checked out the chart, but I don't believe you. (I don't believe there are any, other than the symmetry cases.) Can you give an example?

 

[SparkZer00]

Jaap's diagram shows all the possible shapes (65) up to symmetry of swapping top and bottom, and reflections. If the diagram has top and bottom shapes reversed from what you have, just turn the puzzle over (or turn the diagram upside down). If the shape you have still isn't in the diagram, then its mirror image will be (possibly upside down).

but wouldn't flipping over the puzzle misalign you if you go to execute an algorithm?

But you're not executing an algorithm. You're just going to the next state in the chart. Just align the two faces the proper way and then do a slice move. That should work just as well with the puzzle upside down, right?

there are also the shape possibilities that aren't on that chart

I'm sorry - I haven't ever really checked out the chart, but I don't believe you. (I don't believe there are any, other than the symmetry cases.) Can you give an example?

If I'm correct and my eyes did not fail on me looking at the very small images on the diagram , 5 rows from the top, 15 from the left is a case I'd like to look at. The mirror of the bottom shape of that one, accompanied with the same top shape doesn't show up on the chart, I don't think. For clarity's sake, the shape that doesn't show up is cececcc on top and ceeceeeec on the bottom. The pattern on the chart is cececcc on top, but with ceeeeceec on bottom. The difference is pretty much that the bottom shape is right 4-2 on the chart, and left 4-2 that doesn't appear. I may be wrong, which there is a 75% chance of, and I would love to be, because I really want to learn how to square the square-1 quickly.

Thanks

 

[Lucas Garron]

Jaap's diagram shows all the possible shapes (65) up to symmetry of swapping top and bottom, and reflections. If the diagram has top and bottom shapes reversed from what you have, just turn the puzzle over (or turn the diagram upside down). If the shape you have still isn't in the diagram, then its mirror image will be (possibly upside down).

but wouldn't flipping over the puzzle misalign you if you go to execute an algorithm?

But you're not executing an algorithm. You're just going to the next state in the chart. Just align the two faces the proper way and then do a slice move. That should work just as well with the puzzle upside down, right?

there are also the shape possibilities that aren't on that chart

I'm sorry - I haven't ever really checked out the chart, but I don't believe you. (I don't believe there are any, other than the symmetry cases.) Can you give an example?

If I'm correct and my eyes did not fail on me looking at the very small images on the diagram , 5 rows from the top, 15 from the left is a case I'd like to look at. The mirror of the bottom shape of that one, accompanied with the same top shape doesn't show up on the chart, I don't think. For clarity's sake, the shape that doesn't show up is cececcc on top and ceeceeeec on the bottom. The pattern on the chart is cececcc on top, but with ceeeeceec on bottom. The difference is pretty much that the bottom shape is right 4-2 on the chart, and left 4-2 that doesn't appear. I may be wrong, which there is a 75% chance of, and I would love to be, because I really want to learn how to square the square-1 quickly.

Thanks

But isn't 5-15 the mirror of the shape you're looking for?

 

[cuBerBruce]

Jaap's diagram shows all the possible shapes (65) up to symmetry of swapping top and bottom, and reflections. If the diagram has top and bottom shapes reversed from what you have, just turn the puzzle over (or turn the diagram upside down). If the shape you have still isn't in the diagram, then its mirror image will be (possibly upside down).

but wouldn't flipping over the puzzle misalign you if you go to execute an algorithm?

But you're not executing an algorithm. You're just going to the next state in the chart. Just align the two faces the proper way and then do a slice move. That should work just as well with the puzzle upside down, right?

there are also the shape possibilities that aren't on that chart

I'm sorry - I haven't ever really checked out the chart, but I don't believe you. (I don't believe there are any, other than the symmetry cases.) Can you give an example?

If I'm correct and my eyes did not fail on me looking at the very small images on the diagram , 5 rows from the top, 15 from the left is a case I'd like to look at. The mirror of the bottom shape of that one, accompanied with the same top shape doesn't show up on the chart, I don't think. For clarity's sake, the shape that doesn't show up is cececcc on top and ceeceeeec on the bottom. The pattern on the chart is cececcc on top, but with ceeeeceec on bottom. The difference is pretty much that the bottom shape is right 4-2 on the chart, and left 4-2 that doesn't appear. I may be wrong, which there is a 75% chance of, and I would love to be, because I really want to learn how to square the square-1 quickly.

Thanks

But isn't 5-15 the mirror of the shape you're looking for?

The top shape (I call it "arrow") is the same as its reflection. It's just that the axis of symmetry is not vertical but at an angle in that diagram, so you might not have realized it. All three 5-corner/2-edge shapes are the same as their reflections.

The other shape I call "left candle" (or "right candle" for the mirror shape). So the mirror of "arrow-left candle" is "arrow-right candle."

I also note that the diagram does not show you how to rotate the two layers so that a twist will get to the next row up. You have to figure that out on your own.

 

[SparkZer00]

Jaap's diagram shows all the possible shapes (65) up to symmetry of swapping top and bottom, and reflections. If the diagram has top and bottom shapes reversed from what you have, just turn the puzzle over (or turn the diagram upside down). If the shape you have still isn't in the diagram, then its mirror image will be (possibly upside down).

but wouldn't flipping over the puzzle misalign you if you go to execute an algorithm?

But you're not executing an algorithm. You're just going to the next state in the chart. Just align the two faces the proper way and then do a slice move. That should work just as well with the puzzle upside down, right?

there are also the shape possibilities that aren't on that chart

I'm sorry - I haven't ever really checked out the chart, but I don't believe you. (I don't believe there are any, other than the symmetry cases.) Can you give an example?

If I'm correct and my eyes did not fail on me looking at the very small images on the diagram , 5 rows from the top, 15 from the left is a case I'd like to look at. The mirror of the bottom shape of that one, accompanied with the same top shape doesn't show up on the chart, I don't think. For clarity's sake, the shape that doesn't show up is cececcc on top and ceeceeeec on the bottom. The pattern on the chart is cececcc on top, but with ceeeeceec on bottom. The difference is pretty much that the bottom shape is right 4-2 on the chart, and left 4-2 that doesn't appear. I may be wrong, which there is a 75% chance of, and I would love to be, because I really want to learn how to square the square-1 quickly.

Thanks

But isn't 5-15 the mirror of the shape you're looking for?

no, the shape on the bottom's mirror accompanied by the same top pattern as 5-15 is what I'm looking for

 

[SparkZer00]

Jaap's diagram shows all the possible shapes (65) up to symmetry of swapping top and bottom, and reflections. If the diagram has top and bottom shapes reversed from what you have, just turn the puzzle over (or turn the diagram upside down). If the shape you have still isn't in the diagram, then its mirror image will be (possibly upside down).

but wouldn't flipping over the puzzle misalign you if you go to execute an algorithm?

But you're not executing an algorithm. You're just going to the next state in the chart. Just align the two faces the proper way and then do a slice move. That should work just as well with the puzzle upside down, right?

there are also the shape possibilities that aren't on that chart

I'm sorry - I haven't ever really checked out the chart, but I don't believe you. (I don't believe there are any, other than the symmetry cases.) Can you give an example?

If I'm correct and my eyes did not fail on me looking at the very small images on the diagram , 5 rows from the top, 15 from the left is a case I'd like to look at. The mirror of the bottom shape of that one, accompanied with the same top shape doesn't show up on the chart, I don't think. For clarity's sake, the shape that doesn't show up is cececcc on top and ceeceeeec on the bottom. The pattern on the chart is cececcc on top, but with ceeeeceec on bottom. The difference is pretty much that the bottom shape is right 4-2 on the chart, and left 4-2 that doesn't appear. I may be wrong, which there is a 75% chance of, and I would love to be, because I really want to learn how to square the square-1 quickly.

Thanks

But isn't 5-15 the mirror of the shape you're looking for?

The top shape (I call it "arrow") is the same as its reflection. It's just that the axis of symmetry is not vertical but at an angle in that diagram, so you might not have realized it. All three 5-corner/2-edge shapes are the same as their reflections.

The other shape I call "left candle" (or "right candle" for the mirror shape). So the mirror of "arrow-left candle" is "arrow-right candle."

I also note that the diagram does not show you how to rotate the two layers so that a twist will get to the next row up. You have to figure that out on your own.

I know that, I've used the chart before. The problem is that I don't see a specific pattern, the one with the same top shape as 5-15 (which thank you for pointing out unneccessarily, has the same mirror shape), but a pattern on the bottom that has the mirror of 5-15. I only mentioned 5-15 pattern as a reference for clarity. Obviously that didn't work.

This is all getting off topic anyway, I want to know the squaring method that Lars Vandenbergh's page mentioned

 

[cuBerBruce]

The problem is that I don't see a specific pattern, the one with the same top shape as 5-15 (which thank you for pointing out unneccessarily, has the same mirror shape), but a pattern on the bottom that has the mirror of 5-15.

We tried to explain to you that the diagram does not contain both a puzzle shape and its mirror shape. So it is not going to contain (in Lars's naming convention) both the "Perpendicular edges"-"Right 4-2" shape and the "Perpendicular edges"-"Left 4-2" shape because one is the mirror of the other. (Of course, to get the mirror of a puzzle shape, you mirror BOTH the top shape and the bottom shape.)

The example of a shape you couldn't find was "(Perpendicular edges)-(Left 4-2)". We explained to you that you could not find that shape in the diagram, but you could find its mirror at postion 15-5 in the diagram. So for "(Perpendicular edges)-(Left 4-2)," you use 15-5 in the diagram, even though that's its mirror shape.

The diagram indicates you can get closer to square-square by going to one of these shapes:

cccccee-cececeeee or "Paired edges"-"4-1-1" (which is its own mirror)

ccceceee-ccececee ("Left paw"-"Left fist") and/or its mirror ("Right paw"-"Right fist")

cccccee-cceeeeece or "Paired edges"-"Left 5-1" and/or its mirror ("Paired edges"-"Right 5-1")

(Note that Lars uses the name "Right pawn" for "Left paw" and "Left pawn" for "Right paw." I prefer to refer to them as paws.)

I only mentioned 5-15 pattern as a reference for clarity. Obviously that didn't work.

No, it seemed to me it worked just fine. The pattern you were describing was actually the mirror of the pattern you were using as a reference.