Standard Lettering Scheme for Reference

Universal Rules For Lettering Blind Discussion

Some problems/solutions with all face orders beginning with [UF] are:

1) Starting at U-face and proceeding to F-face will require adding an arbitrary rule just for that, since it does not suffice to say; "go clockwise", when it is clearly impossible to get from the BACK (UBL) to the FRONT (UFL) by going clockwise about the U-face. Therefore an exception rule will be required, that states something to the effect; "now proceed lettering from the U-face to the F-face, by deviating from the consistently clockwise face quadrant lettering scheme, because the transition from U to F feels more natural to some cubers by [x] cube rotation coupled with lettering that mimics the flow of the number "3" when written by hand."

Solution:
U.R.F.L.B.D. (100% Clockwise, 100% Consistent)

2) After U->F-> what comes next? Some say it would be *natural* to proceed next to "L", but others say it is more *natural* for them to proceed next to "R". If we are going to reject the consistent clockwise rule in favor of what is *natural*, then we cannot resurrect it now to arbitrate the decision on which way to go next. It could also be argued that going from F to D could be considered just as *natural*, since we did move by [x] cube rotation in the 1st case (U->F), so why not do it again (F->D)? Here will be another arbitrary choice, without a rational way to support it, other than to say, "some of us agreed on doing it this way". So by beginning with U->F we end up with 3 equally arbitrary possibilities for the starting face orders - UFL,UFD,UFR. So whichever transition is picked, a majority of cubers would probably end up being disappointed with ANY of the face orders starting U->F->X->
Fried pork rinds are *natural*, but that doesn't make them kashrut.

Solution:
U.R.F.L.B.D. (Made with 100% ALL *Natural* RULES)

3) Discussed algs/cases are more likely to have stickers on URF over any other faces. It is nice to get the starting part of the alphabet in sequence with these 3 primary faces. The face order U->F->L skips R so that an inexperienced user of this scheme would have to manually go through the alphabet before they would know that the letter "Q" corresponded with the upper left corner of the R-face. The order [URF] gives the vowels [A-E-I] as the starting letters for those 3 faces. I think beginners trying to familiarize themselves with this lettering scheme would appreciate that rather simple and easy to remember progression. The acronym [URFLBD] will also be helpful in learning and remembering the proper face order.

Solution:
U.R.F.L.B.D. (Easiest to Learn)
 
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The idea is that the face transition for the 4 middle faces is clockwise around the Y axis. You cannot define U->R as clockwise when the face transitions will have to be around more than one axis. Both transitions (U->F, U->R) are equally "clockwise", as they can both be visualized as a downward clockwise spiral:

urflbd.png


Please excuse my MS Paint skills.
 
The idea is that the face transition for the 4 middle faces is clockwise around the Y axis. You cannot define U->R as clockwise when the face transitions will have to be around more than one axis. Both transitions (U->F, U->R) are equally "clockwise", as they can both be visualized as a downward clockwise spiral:

urflbd.png


Please excuse my MS Paint skills.

Both are clockwise, but only 1 is consistent.

Basically what has happened recently is that reThinking pointed out, quite well in my opinion, that the face order UFLBRD violates our rule of ordering everything in a clockwise direction, and in a consistent way. Following the way that we name quadrants always as seen from the top face as moving from the UBL corner to the right toward the UBR corner, then face direction should go the same way. I think we can all agree U is an obvious starting choice. Starting at U the next face we move to in order to stay consistent with not only going always clockwise, but in a consistent way, then we should go right and have the face order URFLBD.

If we are to choose the face order UFLBRD, then let's simply agree on it, and trash the "always clockwise" rule. If we really do want to keep things "always clockwise, and always consistent" then we need to adopt the face order URFLBD to stay with this consistency.
 
Starting at ULB and moving clockwise around the U face, there is only one possible transition, which is to UBR. There is no rule that states that you must move to the right and continue clockwise. Therefore I do not believe that UFLBRD is inconsistent with the given rules, since any face transition from U (excluding D) does not violate this rule, and must be somewhat arbitrary.

Also note that the cube rotation used to transpose F to U's position for the purpose of visualizing the piece ordering is an x move, which is the same move used to visualize the piece ordering on the D face. I could foresee people using a z' move to visualize the lettering on the R face, which would be wrong.
 
I just remembered that the order UFRBLD would fit with my normal scheme, so I'll take back my UFLBRD-vote, and vote for UFRBLD instead.

I don't think we're even voting on that one lol. We at least want the 4 middle faces to be traversed in a clockwise direction.

Naturally.;)

2) After U->F-> what comes next? Some say it would be *natural* to proceed next to "L", but others say it is more *natural* for them to proceed next to "R". If we are going to reject the consistent clockwise rule in favor of what is *natural*, then we cannot resurrect it now to arbitrate the decision on which way to go next. It could also be argued that going from F to D could be considered just as *natural*, since we did move by [x] cube rotation in the 1st case (U->F), so why not do it again (F->D)? Here will be another arbitrary choice, without a rational way to support it, other than to say, "some of us agreed on doing it this way". So by beginning with U->F we end up with 3 equally arbitrary possibilities for the starting face orders - UFL,UFD,UFR. So whichever transition is picked, a majority of cubers would probably end up being disappointed with ANY of the face orders starting U->F->X->
Fried pork rinds are *natural*, but that doesn't make them kashrut.

Solution:
U.R.F.L.B.D. (Made with 100% ALL *Natural* RULES)
 
In response to the bolded text: Beginning with U->R we end up with 2 equally arbitrary possibilities for the starting face orders - URF,URD.

You're just repeating yourself, restating the fact that URFLBD is somehow more consistent than UFLBRD, which I have provided arguments against.

I'm going to do the same thing you do and just repost something I've already said, knowing full well that you've read it already:

Starting at ULB and moving clockwise around the U face, there is only one possible transition, which is to UBR. There is no rule that states that you must move to the right and continue clockwise. Therefore I do not believe that UFLBRD is inconsistent with the given rules, since any face transition from U (excluding D) does not violate this rule, and must be somewhat arbitrary.

Also note that the cube rotation used to transpose F to U's position for the purpose of visualizing the piece ordering is an x move, which is the same move used to visualize the piece ordering on the D face. I could foresee people using a z' move to visualize the lettering on the R face, which would be wrong.
 
I am still tabulating votes, so please keep them coming! I have to leave to go out of town on Tuesday this week, so I will tabulate votes until late Monday evening (early Tuesday morning) EST. After that I'll either post my results here, or give the tabulated info to someone who would like to continue the voting for a longer period.

Sound good?
 
You're just repeating yourself, restating the fact that URFLBD is somehow more consistent than UFLBRD, which I have provided arguments against.

Your arguments prove that you do not understand *yet*, that there is a distinct, and appreciable difference between the various face orders being proposed - in regards to their overall consistency (quadrant face lettering vs. cube face order). Sorry for repeating myself, but when you repeat arguments that have been refuted - you will harvest the repeats of their refutations.

In response to the bolded text: Beginning with U->R we end up with 2 equally arbitrary possibilities for the starting face orders - URF,URD.

This is quite false, and is based on the [z'] premise you posted here.

Also note that the cube rotation used to transpose F to U's position for the purpose of visualizing the piece ordering is an x move, which is the same move used to visualize the piece ordering on the D face. I could foresee people using a z' move to visualize the lettering on the R face, which would be wrong.

The 1st part of that post is correct. When you [x] cube rotate UBL (the 1st face quadrant of the 1st face U) maps directly to FUL(the 1st face quadrant of the 2nd face F). I take this to be a negative, in that - UFD might become the next assumed face order in this case. That is one of the problems with having a face order beginning with U->F.

Face order beginning U->F yields 3 or more arbitrary and inconsistent possibilities: [UFLBRD,UFDBRL,UFRBLD]

The 2nd part (which I bolded) is incorrect. When you [z'] cube rotate UBL (the 1st face quadrant of the 1st face U) does NOT map directly to RUF(the 1st face quadrant of the 2nd face R), but instead it maps to RBU. This is a positive, since in this case, there can be no false assumption that a [z'] cube rotation is the reason for the face order. That is one of the advantages of having a face order beginning with U->R.

Face order beginning U->R yields 1 consistent rule based possibility: [URFLBD]
 
reThinking the Cube: Get your cube rotations right.

I don't want to argue against you because it'll achieve nothing (and I do think you have some validity), but please concede that there is some measure of arbitrariness in any of the orderings proposed. Some of your arguments might as well be used against you.

(Personally, I think riffz is right with his cube rotation comment.)
 
reThinking: I still disagree with you, and I find it annoying that instead of elaborating, you simply state that I do not understand and that you will continue to repeat yourself. I think, however, that we are not going to convince the other to change their stance on this issue, so I will not be debating you further on this.

Please be aware that I do not think that UFLBRD is any more correct than URFLBD. I understand your reasoning for choosing it, but as Lucas said, any face ordering will be somewhat arbitrary. ("Clockwise" simply doesn't describe how to traverse the 6 faces of the cube in 3 dimensions.) In this case, I see no problem with choosing the face that feels most natural, since I do not believe that either choice violates the established rules.
 
reThinking the Cube: Get your cube rotations right.

I don't want to argue against you because it'll achieve nothing (and I do think you have some validity), but please concede that there is some measure of arbitrariness in any of the orderings proposed. Some of your arguments might as well be used against you.

(Personally, I think riffz is right with his cube rotation comment.)

I wish I could also agree with riffz on this, but unfortunately that cube rotation comment is based on a misconception. The RUF face quadrant is not replacing the UBL face quadrant by a [z'] cube rotation. It actually would require [z' y] to do that. I really don't want to argue against any of you, but I do hope this explanation helps you get YOUR cube rotations right.:p

I will also concede, that most rules have some measure of arbitrariness, and requiring more rules, will make just about anything more arbitrary.
 
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Has anyone taken the assignment to come up with drawings for 5x5x5 and 7x7x7 full lettering scheme?

I can do it, but it will look as beatiful as on the second page:
x is also before z in the alphabet ;)

Mike: we were talking about the first corner being ULB.

Maybe this will clarify things:
5x5lettering.png


(in Aron's image the F and R faces were visible)

I really have not read all the thread and ask: Yellow on top, red in front?


Peedu
 
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