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 Post subject: How To Solve Timur's Biaxe
PostPosted: Thu Sep 05, 2013 5:00 am 
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Joined: Sun Aug 26, 2012 10:01 am
Solving Timur's Biaxe

Because Timur and luckyguynt are producing the Biaxe, I thought a solving thread would be a good idea! You can play with the puzzle by downloading the software here. It’s the 3dcube32.rar file. You’ll have to email the email address given on the site to unlock the program.

This is my method in solving Timur's Biaxe Puzzle :)

1. Solve the corners very easily by rotating them into place; they only need to be orientated.

2. Solve the star points, (making sure I solve them to match the corners when using set up moves) using [R L' R' L R' L R L R' L' R L R 2L R' L' R]x4. This is the hardest part of the solve in my opinion because the set up moves can be VERY difficult to set up.

3. Solve the edges using this 3 cycle (of the edges on the front face, which makes any required set up moves easy (again, in my opinion)): [R' L R L']x7

4. Solve the centers using this 2-2 swap: [R' L R L']x21.

You might have noticed yourself, but the algorithm for the edges and the centers are both the same, just repeated a different amount of times. The [R' L R L']x7 which is used for solving the edges is a 3 cycle of edges AND a 2-2 swap of the centers which is fine however because we solve the centers afterwards because they're easier to set up. If we call ([R' L R L']x7) Y, then 3Y would cancel out the 3 cycles and leave a 2-2 swap.

They won't be required when solving because they're solved first, but I decided to find pure corner twisting algorithms:

Rotate both corners 90 degrees: [L R' L R L R L R' L' R' 2L]x4

Rotate the right corner 180 degrees: [L R L' R]x105


When using the software, the notation for inputting is as follows:

R=3

L=1

So if you want to type in an algorithm, you must replace all R’s with 3’s etc.

Also using ( )xY doesn’t work, you have to click the “run alg” button Y times.

Now for your convenience, here are the algorithms with the 3’s and 1’s:

Cycle 3 points: (31'3'13'1313'1'313113'1'3)x4

2-2 Swap centres: (3'131')x21

Cycle 3 edges: (3'131')x14

Rotate 2 corners 90 degrees: (13'131313'1'3'11)x3

Rotate single corner 180 degrees: (131'3)x105

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 Post subject: Re: How To Solve Timur's Biaxe
PostPosted: Wed Jan 22, 2014 7:13 pm 
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Joined: Fri Feb 18, 2011 5:49 pm
Location: New Jersey
I'm surprised this thread doesn't have any other replies yet! The biaxe was a pretty tough solve for such a small puzzle.

Here's my method:

1. Twist corners to fix orientation
2. Solve centers with simple 2-2 swaps: R' L R L'
3. Solve edges with 3-cycles: (R' L R L')x2
4. Solve the star-points with 3-cycles: [x,y]

x:
R2 L R2 L R2 L2 R2

y:
R' L2 R'
(L2 R' L2 R)x5
R L2 R

Although my 3-cycle algorithm is technically slightly shorter (61 moves versus 65 when you consider move-cancellations), I think Jack's is much easier to remember and use...

Jack, I'm surprised you don't solve the star-points last as well, since your algorithm is pure too. Solving them last makes the edge and center algorithms much much shorter. Also, I think having the other pieces already in place makes finding and undoing setup moves a lot easier for the star-points. Also, solving the edges and centers is so fast it's hardly a noteworthy loss of "investment" if you mess up the star points afterwards.


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 Post subject: Re: How To Solve Timur's Biaxe
PostPosted: Wed Jan 22, 2014 7:43 pm 
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Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Don't the small triangles come in two orbits?

My plan is 1) corner orientation, 2) edges, 3) centers, 4) the rest

The first three steps are short and easy but I don't have anything good for "the rest". I've been looking for something elegant without much luck yet.


Edit: I should mention that at some point I'm going to get around to programming it too. It has too many states for fully enumerate god's algorithm but with a pruning table for the other pieces it should be easy to search for pure cycles in the triangles. With only two axes I should be able to search to a depth of ~20 or so.

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 Post subject: Re: How To Solve Timur's Biaxe
PostPosted: Thu Jan 23, 2014 1:28 am 
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Joined: Sun Aug 26, 2012 10:01 am
I haven't actually solved the biaxe, I just decided to see if I could find the algorithms necessary to do so due to the small production of then.

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 Post subject: Re: How To Solve Timur's Biaxe
PostPosted: Thu Jan 23, 2014 5:50 pm 
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Joined: Fri Feb 18, 2011 5:49 pm
Location: New Jersey
I found an even shorter 3-cycle:

In full commutator/conjugate form it looks like it should be 52 moves:
((R2 L' : (L' , R2)) (L2 R2 L' : (L' , R2)) , (L2 R : (L2 R)))

But when you expand it, a lot of turns cancel out or combine and it's actually only 38 moves:
R2 L2 R2 L R2 L R2 L2 R2 L2 R2 L R2 L R' L2 R L R2 L' R2 L2 R2 L2 R2 L' R2 L' R2 L2 R2 L2 R2 L2 R' L2 R' L2


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 Post subject: Re: How To Solve Timur's Biaxe
PostPosted: Sat Feb 22, 2014 8:43 pm 
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Joined: Thu Mar 28, 2013 7:14 pm
I just got mine! Quickly discovered the edge 3-cyles and center swaps as previously described. Kinda stuck on the star points but I'll figure it out. What a great little puzzle. Just two turning axes and it's a killer!


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 Post subject: Re: How To Solve Timur's Biaxe
PostPosted: Thu Mar 27, 2014 4:45 pm 
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Joined: Sat Oct 29, 2011 9:28 am
Location: Sweden
Hi!
I also think this is a great little puzzle and today I finally find out how to 3 cycle these star points.
As said here before it's quite easy to solve the edges and centers. Here is my solution for the star points:

[x:y]

x: (R' L R L')x6 or (R L' R' L)x6

y: R' L' (2R L' 2R L)x5 L R

I think it's quite easy to remember and use backwards and mirror it.

/Andreas Andersson


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