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Solving 6x6-7x7 oblique centers

cmhardw

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I posted this in the V-cubes thread, but if anyone else is interested here is how I thought about those "oblique" centers for my 6x6x6 BLD solve.

------------------------
We're calling those the "oblique" centers. They are by far the hardest thing about solving the bigger cubes blindfolded, in my opinion at least.

My definition of the types of pieces, for the 6x6x6 since it's the only one I've tried obviously, are the
1) corners
2) inner wings
3) outer wings
4) inner x-centers
5) outer x-centers
6) "clockwise" oblique centers
7) "counter-clockwise" oblique centers

The 7x7x7 has all the same pieces, but add to this
8) inner t-centers
9) outer t-centers
10) central edges (like on a 3x3x3)

Ok, so for oblique centers I tried 3 different things for each of my 3 different solves as to how to visualize them.

First solve I tried to think of them purely in the abstract sense. I imagined them as having coordinates in a matrix (in a 6x6 matrix, since each face has 36 stickers, or "entries"). This does not work well for the B and D faces, and I did DNF my first solve, mostly because of centers, so I don't recommend this method.

Second solve I tried to think of them as numbers of layers away from the corners. The notation I will be using was mentioned before on the speedsolving yahoo group, but if a better one is developed I don't mind switching.

The layers, as seen from left to right (L and R) are:
L l1 l2 r2 r1 R

for a 7x7x7 it would be
L l1 l2 m r2 r1 R

So anyway the oblique center at [U l2 b1] is my "A" piece for the "clockwise oblique centers". This is because, as seen from the outer x-center oribt (the piece at [U l1 b1]) I would have to rotate clockwise one piece (inside the 2x2 grid of each of the different kinds of x-centers) to get to it.

But look at the definition of the piece I gave you [U l2 b1] that means, from the corner at UBL I would count over 2 slices to the right (placing me on the l2 slice) and one slice toward me (placing me at b1). You do the same on other faces.

I DNF'd my second solve too, also partially due to centers, and I don't recommend this second method either.

Ok, the solve I got I pictured the oblique centers completely visually. I liked this method so much that it is what I will use in the future. Although I define the oblique centers in 2 groups, clockwise and clockwise groups of them, when solving I picture them visually.

So for example on any given face, when looking at all of the clockwise- and counterclockwise-oblique centers you will see that there are 8 of them per face. Let's say we are looking at all the oblique centers on the U face.

They, all 8, are at:
[U l2 b1]; [U r2 b1] (all on the b1 slice)
[U l1 b2]; [U l1 f2] (all on the l1 slice)
[U f1 l2]; [U f1 r2] (all on the f1 slice)
[U r1 f2]; [U r1 b2] (all on the r1 slice)

Ok, notice that they come in pairs of 2 on each of the b1, l1, f1, and r1 slices. When solving I think of them by these pairs. First I decide which of those 4 pairs it cycles to - basically just think does it cycle to the "top" of the face, the "left" of the face, the "right" of the face, or the "bottom" of the face. Then, upon deciding that you have to visualize which of the 2 pieces is interchangeable with your buffer. To do this I imagine how I would move my buffer to that pair of pieces. I think with more practice that I would eventually work to just memorize which piece is the "clockwise-oblique" and which is the "counter-clockwise-oblique" for each pair, but for a first solve this is how I did it. It works very quickly, very easily, and that is the only solve of the 3 I solved successfully.

So when you are working on those oblique centers, that's how I recommend to do it.

-------------------------------------------------

Good luck everybody, I hope to join the fun when I get back from my trip!
 

masterofthebass

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masterofthebass
#2
When I get my cubes, I'm definitely going to take a look at how to solve these. For some reason, I'm not really looking at them as that hard of a challenge, as I basically have looked at them as the way you look at them in your 3rd method. I know which centers are interchangeable with just a face turn, and that allows me to be able to use them. So.. for my letter scheme on the 6x6 i'm thinking of this :

A A A B
D A B B
D D C B
D C C C

I go clockwise around the U face, so I really would just picture them as the l-slice oblique or the r-slice oblique (when looking at the "back" row).
 
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blahcel
#3
I'd do exactly the same as Dan. In fact, that's the most natural and the only way I've ever thought of for solving these oblique centers. I don't have a V-Cube and I haven't ordered them, but I've been thinking about how to solve 6x6x6 and 7x7x7 blindfolded and I don't think I'd have a problem solving the oblique centers at all by just using the normal commutators I use for "smaller big cubes", or am I missing something?
 
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PedroSG
#5
When I get my cubes, I'm definitely going to take a look at how to solve these. For some reason, I'm not really looking at them as that hard of a challenge, as I basically have looked at them as the way you look at them in your 3rd method. I know which centers are interchangeable with just a face turn, and that allows me to be able to use them. So.. for my letter scheme on the 6x6 i'm thinking of this :

A A A B
D A B B
D D C B
D C C C

I go clockwise around the U face, so I really would just picture them as the l-slice oblique or the r-slice oblique (when looking at the "back" row).
same as I tought, though I don't use letters
and I go like
1 2
3 4

but I think I can "see" the different types

well...I just tried the 5x5x5 once, so I may not be a good opinion :D
 
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#6
It makes so much more sense to order them:
A A A B
D A B B
D D C B
D C C C

Certainly, it extends better for bigger cubes. I think a lot of people (including myself) are stuck in the habit of numbering it top->bottom, left->right. For this orbital it sure seems strange:
x x 1 x
2 x x x
x x x 3
x 4 x x

I'm pretty sure Hardwick numbers "top->bottom, left->right" as well.

But to be realistic I will probably never try and BLD a 6x6.


-Doug
 
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#7
I use the same lettering scheme as Dan:
+=the center center (as on 5x5 and 3x3 and 7x7)

4x4:
a b
d c

5x5:
a a b
d + b
d c c

6x6:
a a a b
d a b b
d d c b
d c c c

7x7:
a a a a b
d a a b b
d d + b b
d d c c b
d c c c c
 
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#8
Hi :)

I attach an image showing the center cubie orbitals for a 6x6x6 cube.


Only same color centers can be interchanged.

- Per
 
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#13
Wouldn't it perhaps make sense to break everything down into quadrants on the 6x6??

1122
1122
3344
3344

Like the whole mathematical concepts of a graph, and its 4 quadrants?

II | I
---.---
III | IV

of course for the odd numbered cubes its a little different but there are different methods to madness that can be used.


For the t-centers on the 5x5 and 7x7 (the "|" and the "-" in the representation of the graph)

I number them
-1-
2.3
-4-

On the 7x7 if you number the two t-center orbits with the scheme above, you will still have the 6x6 quadrants.

Just sharing my wealth of knowlege, or as others may say, my 2 cents :)
 
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#15
11y22
11y22
xxc++
33-44
33-44

1,2,3,4 = x-centers and obliques
y,x,+,- = two t-centers orbitals

For the F face,
I'd letter

For x-centers and obliques the 1s would be lettered "D"
For the t-centers the ys would be lettered "D"

2s and xs would be lettered "E"
3s and +s; "F"
4s and -s; "G"

You are right ... I'm just so used to the Left Right, Top Down scheme of english and my lettering scheme I messed it up :p
 
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