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 Post subject: Notation For Dodecahedron Puzzles
PostPosted: Sun Dec 11, 2011 10:34 am 
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Hi Friends,

There are different notations for megaminx like puzzles.

My Idea:
Attachment:
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The dodecahedron stands on ground; you look towards "F".

The upper face is U. U is parallel to the ground.

The upper right face is in upper case R
The lower right face is in lower case r
The upper left face is in upper case L
The lower left face is in lower case l

D ( down ) is in opposite from U.
B ( back ) is in opposite from F.


This describes all visual face and 2 more faces.

The last 4 faces can described with OR OL Or Ol
Opposite Right Upper.
Opposite left lower.

Y Turning the dodecahedron clockwise.


My idea was a compromise between intuition and less letters.

What do you think about this notation ?
I will use it private; I don't use a simmulator.
For finding commutators, conjugators and fast write down sequences perhaps this notation is ok.

Cheers,
Andrea


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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Sun Dec 11, 2011 10:59 am 
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Hi,

by example the face turning starminx.
It's an advantage to define slice twists.
Its difficult to describe slice turns with turning the whole puzzle.

For slice turns I would use the letter m or M.
I saw similar definitions in the Rex Cube thread.
M R turns the slice adjacent the upper right face in the same direction as the right face.

Perhaps it's a advantage specifically for the faceturning starminx to define antislice movements.

I would give the letter "a" for antislice.

a R twist the upper right face clockwise and the opposite clockwise, too.

This are only proposals.

Cheers,
Andrea


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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Sun Dec 11, 2011 3:57 pm 
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The Gelatinbrain notation is not intuitive, therefore my notation (to your right) uses more intuitive names like L for left:

Image

I name inner slices after the adjacent outer face and use l, r, f like in the WCA notation.
(Gelatinbrain uses A&2 for the slice under A)

In most cases my move sequences use just L, R, F. The two letter names (e.g. DR = Down right) are very rarely necessary.

Gelatinbrain has the advantage that you can unambiguously post a sequence that a reader can cut and paste into the Java applet.

You can either download the Gelatinbrain program (unfortunately it does not run on my computer) or use a browser to run the applet online.

Whenever I post a move sequence for a Dodecahedron I post it together with my (personal) notation.

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Last edited by Konrad on Sun Dec 11, 2011 4:59 pm, edited 1 time in total.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Sun Dec 11, 2011 4:45 pm 
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I made a post about megaminx on the Speedsolving forum, and I started off with my idea for notation. I'm just throwing it in here for reference. I didn't mention anything about slice turns since I didn't see myself using it anytime soon (it was mainly intended for megaminx), but if I did I would prefix any turn which wasn't of the outer layer only with the slices being affected. Eg. 2R would be the second layer parallel to the R face, and 2,3R would be the 2nd and 3rd layers. I believe something similar is already in use in one of the notations for big cubes.

Obviously I personally think it's a nice notation, but I don't see any notation being well-known and standard any time soon which deals with all FT dodecahedrons, but I would like to see one.

Matt S


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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Sun Dec 11, 2011 4:46 pm 
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HI Konrad,

thanks for your pictures. I would prefer your pictures on right side.
Konrad wrote:
Whenever I post a move sequence for a Dodecahedron I post it together with my (personal) notation.


Yes, this is important.

To understand sequences it's often easier to change the visualization and notation.

Cheers,
Andrea


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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Mon Dec 12, 2011 1:55 am 
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Hi Friends,

I think it would be a great thing to have a common `colloquial` notation. I will put forward an idea that I think is a combination of what I do privately and what is written here. I can see a recognition problem with some combinations of upper and lower cases and such. I have tried to put forward an intuitive format.

I think it would be preferable not to use any underlining (because it’s not fast to type) or lower case (because it’s used for slice turns) in the face descriptions. WCA notation (using the respective lower case letters) is an excellent way to identify slice turns, where for example: u and d’ are the same thing on the FT Starminx. And of course (‘) identifies an anticlockwise twist. And numbers (2,3) are most commonly used to identify the amount of turns. A space can be left in the notation between turns to identify the next turn (because multiple characters are being used).

I see that it is better to write less characters to describe a face, but I also see that where I have used 3 letters, these are very uncommon faces.

So a sequence might look like: (u 2dr’ u’ 2dr) 2U’ (2dr’ u 2dr u’) 2U

What do you think?

Cheers,
Burgo.
PS: Another option would be to use
UL & UR instead of BL and BR and therefore
BL & BR instead of DBL & DBR
but I think that is less consistent with notation for the cube, and therefore less intuitive.


Attachments:
Dodec notation.jpg
Dodec notation.jpg [ 181.09 KiB | Viewed 4891 times ]

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Mon Dec 12, 2011 3:44 am 
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Hi Burgo,

I think most people will agree on the assignment of U, F, R.
Our two notation are close to each other. I did not like the R and L notation myself (fortunately I never needed them for any of my move sequences)
DR instead of Dr is not a big difference.
I would vote for your alternative with UL and UR avoiding three letter names.

What about slice moves?
I vote for lower case notation like u, f, l and r turning clockwise as U, F, L and R (l' , r' etc. for counterclockwise) for the slices below the outer faces.
2R could be a synonym to r (I would stick with r because it is shorter).
3R for a third layer.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Mon Dec 12, 2011 5:47 am 
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Hi Konrad (and others),

It’s nice to have an open discussion about it.

The sequence I used as an example has slice turns & face turns, single turns & multiple turns.

Yes, Dr to DR is a small change, I think it distinguishes between slice turns and face turns better.
I would prefer to see lower case rather than a number to indicate the next slice in (like you), and then possibly a prefix like:
2DR’ (face) then 2dr’ (slice) then 2*dr’ (2nd inner slice) then 2**dr’ (3rd inner slice)
and to turn all 3 together: 2DR’+2dr’+2*dr’ or shorthand 2DR’+dr+*

My thinking for face naming was:
I don’t like the 3 letter names much either, but I considered what would be intuitive for an outsider who did not know the notation (also consider: a lot of dodecahedron sequences have similarities to cube sequences). I think in respect to the cube: the blue & white faces (in my diagram) are associated with the Back Cube Face, and the grey & light blue faces are associated with the Down Cube Face. We could use any letter for the pink & dark green faces, but what would an outsider intuitively recognise? So I fell back on the 3 letter description. I thought: it’s nicer to pay respect to the cubic equivalent with the faces we more commonly use, such as the upper half. I just don’t think that the DBR face turns are important enough to make a less intuitive symbol for it (if that makes sense). But I'm happy to use what the consensus is :D .

The thing that will be difficult to name will be the axis rotations. The y axis is fine, but no others. Maybe we should call it by face, like: F(axis) or 2R(axis)’ what do you think? Or do you think we will only need y?

Cheers,
Burgo.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Mon Dec 12, 2011 5:55 am 
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Hi guys.

a very worthwhile thread.

After reading your postings I came up with this:
Attachment:
DodecahedronNotation.jpg
DodecahedronNotation.jpg [ 28.34 KiB | Viewed 4847 times ]
I tried the same you others tried: to adapt Singmaster's notation. I remembered how a hexaminx is made from a megaminx: by defining six edges as the new puzzles sides. I did the same here and afterwards labeled the adjacent faces with Singmaster letters and gave them an additional letter to differentiate the two faces for each edge from each other.
After I read again Burgo's point about the slice moves I changed the names to all-capital. Before I used one capital and one following lower case letter.
Advantages:
1. All sides are labeled uniformly.
2. After you understood that U, D, etc. denote an edge the system is intuitively.
3. The notation even defines how to hold the dodecahedron correctly.
4. Opposite faces are easily identified.
5. Easily defined slice moves: uf equals db' as everyone would expect.
Disadvantages:
1. Two letters even for those faces which are most often turned.
2. Not perfect for Gelatinbrain since it implicitly defines that an edge is in front not a face.

Andreas


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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Mon Dec 12, 2011 7:29 am 
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Andreas Nortmann wrote:
Hi guys.

a very worthwhile thread.

...
1. All sides are labeled uniformly.
...
Yes, but in my view single letters for most commonly used faces outweigh this.
It is more intuitive for me to look at a dodecahedron sitting on a table, one face looking at me and now I ask myself what should become U, F, L, R. This is a pretty obvious choice, right?
Now saying B is opposite to F and D is opposite to U is pretty close too.
Now we have used all six letters of Singmaster notation and the other six should be two or three letter names.
Here is my proposal (Burgo's alternative):
Image

UR and UL are intuitive for me: In the upper part right and left.
I would prefer to say DBR and BR are synonyms but because BR is unique we use the shortcut BR.

Two clockwise turns U U should become the shortcut U2, two anticklockwise moves U' U' should be U'2.
Inner slices are named by lower case letters: u, u2, u'2
(2U is misleading in my view and unnecessarily different to the usual (WCA) cube notation.)

Now, how do we name more inner slices?
A number prefix is used in different notations differently. In WCA notation 3U means three layers turned together.
In other notations 3U would denote the third layer below U.
Therefore, I would use something different like in Gelatinbrain: R&2 could be a synonym to r.
Following this R&3 could be the third layer below R.

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Last edited by Konrad on Mon Dec 12, 2011 7:38 am, edited 1 time in total.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Mon Dec 12, 2011 7:32 am 
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I think I'm swinging towards `this` like Konrad, the single letters for the common faces are already in common use, and I didn't like the 3 letter face names either. This has my vote too.
Cheers,
Burgo.


Attachments:
Dodecahedron Namenclature.jpg
Dodecahedron Namenclature.jpg [ 171.46 KiB | Viewed 4825 times ]

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Mon Dec 12, 2011 7:47 am 
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I like the idea of the & sign to denote `as well as`, so to me it sounds like 3&F would mean `all 3 layers on F`, so 3&F2' would mean `all 3 outer layers on F turned 2 turns anticlockwise`.
Whereas 3F sounds more like the third layer in on the F face, and 2F is equivalent to f.

That makes sense to me, what do you think?
Cheers,
Burgo.

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PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Mon Dec 12, 2011 8:07 am 
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Seems like not everybody sees the cube inside a dodecahedron.
Konrad wrote:
It is more intuitive for me to look at a dodecahedron sitting on a table, one face looking at me and now I ask myself what should become U, F, L, R. This is a pretty obvious choice, right?
No. I consider it counter-obvious because it leads to l<>r'.
L is not opposite to R and therefore the slices under them are not equal. Same is true for BR and BL.

my 2 cents.


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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Mon Dec 12, 2011 8:27 am 
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Andreas Nortmann wrote:
Seems like not everybody sees the cube inside a dodecahedron.
Konrad wrote:
It is more intuitive for me to look at a dodecahedron sitting on a table, one face looking at me and now I ask myself what should become U, F, L, R. This is a pretty obvious choice, right?
No. I consider it counter-obvious because it leads to l<>r'.
L is not opposite to R and therefore the slices under them are not equal. Same is true for BR and BL.

my 2 cents.
Yeah, but just looking for a right face at MY right and a left face at MY left leads to my choice.
It is interesting that many different people came up with this, independently. This seems to be some proof what people see as intuitive.

What do others say?

EDIT:
P.S. Andreas, I understand that your proposal is very satisfying for an abstract, mathematical mind like yours. :)
(Please, do not misunderstand this as ironic. I want to express my full admiration for your theoretical considerations in other threads. :) )
Others may have difficulties to understand the reasoning behind the face names at the first glance.
On the other hand, it is easy to grasp why L and R are assigned to faces at your right or left hand, even if they are not opposite to each other.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Mon Dec 12, 2011 11:42 am 
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Burgo wrote:
I like the idea of the & sign to denote `as well as`, so to me it sounds like 3&F would mean `all 3 layers on F`, so 3&F2' would mean `all 3 outer layers on F turned 2 turns anticlockwise`.
Whereas 3F sounds more like the third layer in on the F face, and 2F is equivalent to f.

That makes sense to me, what do you think?
Cheers,
Burgo.
I would vote to go along with WCA and use 3U as `3 layers including U`.
This could be written as a superscript number above the baseline whenever it is supported by your word processor (obviously not here). Burgo, you will remember this from my Professor Pyraminx tutorial.

What about `U#3` as `U layer number 3` and U#2 being a synonym for u?

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Tue Dec 13, 2011 2:08 am 
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Konrad wrote:
What about `U#3` as `U layer number 3` and U#2 being a synonym for u?
Notation for individual layers is also not uniform :( . It would be my thinking to use whatever is in most common usage to avoid confusion. That being said, you need to distinguish between the `number of turns` and `the number of layers`. In the example you suggest here, the number of layers is on the right of the face name. This makes it hard to distinguish succinctly between turns and layers. Whatever we suggest I think the number of layers needs to be on the left side and the number of turns on the right side of the face name.

In my private notation I don't use numbers, I use:
R2' for turning the outer face
r2' for turning the inner slice (so far normal)
Rr2' for turning both layers together (and I stop here)
rR2' could be an acceptable variant
#3R2' (a slight variation of your suggestion) could represent the 3rd slice in- that's nice, I vote for it.
3*R2' then makes sense as all 3 outer layers turned (* is multiply)
3R2' is an obvious variant of this (WCA notation)
This would be a very efficient (and sensible/ intuitive) way of writing it, which is just what we want :D .

What do you think about the axis turning? I made a suggestion above ^^
I don't like the `word` axis (as I wrote above), what is a good symbol for it?
Maybe we could use opposite faces to denote it (and this would determine direction), for example:
y = U/D (in the direction of U)
y' = D/U (in the direction of D)
What do you think?

I too understand Andreas' suggestion for face names and see how it accounts for opposite faces, but unfortunately I agree that it is not intuitive or related to common usage. Thanks for your suggestion Andreas, many ideas and opinions are good :D .
I think we almost have something complete.. maybe we could take it to some kind of community vote when it is done?
Cheers,
Burgo.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Tue Dec 13, 2011 5:12 am 
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Hi Burgo,

Quote:
I too understand Andreas' suggestion for face names and see how it accounts for opposite faces, but unfortunately I agree that it is not intuitive or related to common usage.


Yes, you're right. I agree. This was my first idea. I thought about it.
It's confus to use lower case letters for slice turns. Better it's to use numbers like big cube notation 3R 3L etc.
or if only one slice exist MR ML MU etc. ( for each puzzle)

<bad idea>
I know, that the pentagon diagonals define the edges of a cube. Using this is more confusing because the dodecahedron lies not parallel to the ground, this was not intuitive because thinking about sequences the dodecahedron stands on the table. A second disadvantage was that all faces had double letters like RU LU FD etc. So I had not posted this idea to this forum.</bad idea>

I like your notation from Mon Dec 12, 2011 1:32 pm !

Cheers,
Andrea


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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Tue Dec 13, 2011 6:23 am 
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Andrea wrote:
...It's confus to use lower case letters for slice turns. Better it's to use numbers like big cube notation 3R 3L etc.
or if only one slice exist MR ML MU etc. ( for each puzzle)
I think Burgo, Andrea and I agree on the names of outer faces. Burgo's and my last pictures describing it are identical.
Regarding inner slice moves:
I clearly vote to stay close to the WCA notation for big cubes:
Lower case letters for the layer under an outer face!
I have read and used this since the early 80's and WCA is a standard.
I vote for Burgo's proposal:
A prefix and a number sign: 3#U = third layer of U.
We define 2#U as a synonym for u. (This allows people like Andrea to avoid lower case names :) )
3*U would be three layers together and this can be a synonym for 3U (as in WCA)
3*U would be clearer, because it cannot be misunderstood as SIGN notation (In SIGN 3U is the third layer.) I have nothing against SIGN, I'm just familiar with the lower case letters for all my cubing live.
When the first 4x4x4 came out, the Singmaster notation was widespread and it seemed quite natural to use the lower case letters for inner layers below an outer face. At least it was a natural choice for me and many others.

Regarding the turns of the whole puzzle around an axis:
I vote to write it like a function like A(U) meaning ' a turn of all pieces (the whole puzzle; A = 'all pieces') around an axis going through the centre of U'.
Andrea wrote:
I like your notation from Mon Dec 12, 2011 1:32 pm !

Cheers,
Andrea
Right, this picture is identical to my last picture for the Starminx :)

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Tue Dec 13, 2011 6:53 am 
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Hi Konrad,
Konrad wrote:
A prefix and a number sign: 3#U = third layer of U.
It `sounds` better to write #3U because saying it out loud is like: Number-three U whereas 3#U is like saying: three-number U (which sounds wrong).

Yes, I think it is good to use * to distinguish because it avoids confusion. 3*U is the correct `sounding` way to write this one (three-lots-of U).

Quote:
I vote to write it like a function like A(U) meaning ' a turn of all pieces (the whole puzzle; A = 'all pieces') around an axis going through the centre of U'.
Has this been used before in other notation?
So: you would write A(U) and [A(U') synonym A(D)]
I like it the same as what I suggested, either is nice and short and intuitive, mine was a bit shorter: U/D
I would be happy to use either.
Actually, I think yours is better because it would work for a cube with no opposite face, like a pyraminx.

Cheers,
Burgo.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Tue Dec 13, 2011 7:43 am 
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Burgo wrote:
...It `sounds` better to write #3U because saying it out loud is like: Number-three U whereas 3#U is like saying: three-number U (which sounds wrong).
Agreed!
Burgo wrote:
Yes, I think it is good to use * to distinguish because it avoids confusion. 3*U is the correct `sounding` way to write this one (three-lots-of U).

Quote:
I vote to write it like a function like A(U) meaning ' a turn of all pieces (the whole puzzle; A = 'all pieces') around an axis going through the centre of U'.
Has this been used before in other notation?
So: you would write A(U) and [A(U') synonym A(D)]
Yes. Actually I would allow y as a synonym for A(U). Honestly, I have never needed to write down an axis turn for my dodecahedra other than y!
Burgo wrote:
I like it the same as what I suggested, either is nice and short and intuitive, mine was a bit shorter: U/D
I would be happy to use either.
Actually, I think yours is better because it would work for a cube with no opposite face, like a pyraminx.

Cheers,
Burgo.
Interesting , that you call the Pyraminx a cube. :lol: Same for me, I'm always talking about non-cubic cubes :lol:

Now, what is the result of this discussion? I mean we are no standard committee. If just Andrea, you and me are using it, it does not change much.

Maybe, even Andreas is not really happy with it?
I think that only five people have contriuted here.
I would still provide together with any hint the notation I'm using.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Tue Dec 13, 2011 4:32 pm 
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Konrad wrote:
Now, what is the result of this discussion? I mean we are no standard committee. If just Andrea, you and me are using it, it does not change much.
Hey Konrad, I like you notation so I have added it as an output option to my sequence processor:
http://www.brandonenright.net/cgi-bin/gb_util.pl

I don't yet take your notation for input. I suspect a lot of people will want to discuss Starminx solving soon so it seems like a reasonable thing to support.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Tue Dec 13, 2011 5:02 pm 
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bmenrigh wrote:
...

I don't yet take your notation for input. I suspect a lot of people will want to discuss Starminx solving soon so it seems like a reasonable thing to support.
Hi Brandon, this is really cute :)
I tested it with the Pentultimate sequence mentioned in my post today in the Starminx thread and with a commutator using slice moves Nice work! Thank you!

The credit for the result of this discussion goes to Burgo as well and to Andrea for starting this thread :)

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Wed Dec 14, 2011 5:47 pm 
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Hi Konrad and others,

I think what is left to do is to make a final post with all of the `finalized notation` so people don't have to read the entire thread (and to avoid confusion). Maybe Andrea can then copy it and put it in the top part of the first post also?

One thing that is missing is a name to refer to it with. TPD Notation (Twisty Puzzles Dodecahedron) for example.

One last thing. I think that it has as its strong point, flexability to be used and understood along with other notations, actually I will adopt it in my private notation (and probably forum posts) for layers on cuboids too. Being able to say E layer or u layer & y or A(U) adds greater flexability. (Like saying 1 or one).

bobthegiraffemonkey wrote:
I don't see any notation being well-known and standard any time soon which deals with all FT dodecahedrons, but I would like to see one.
It would be nice wouldn't it Matt :D

One last thing, I have noticed that:
U'2 has replaced U2'
in the posts on the FT Starminx thread. I don't understand why (I see it as an acceptable variant), but all other cubic notation uses the apostrophe on the end, why are you using it after the face name for dodecs? Is it from Gelatinbrain notation?

Cheers,
Burgo.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Wed Dec 14, 2011 5:54 pm 
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Burgo wrote:
One last thing, I have noticed that:
U'2 has replaced U2'
in the posts on the FT Starminx thread. I don't understand why (I see it as an acceptable variant), but all other cubic notation uses the apostrophe on the end, why are you using it after the face name for dodecs? Is it from Gelatinbrain notation?


U'2 instead of U2' is due to Gelatinbrain but I think it is easier to think of it that way anyways.

The syntax is <name><direction><amount><slice mask>

Where <name> is {A, B, C, ...} and <direction> is either blank or ' and <amount> is a number and the slice mask is option but takes on the form &<bitmask> where bit 0 (1) is the face, bit 1 (2) is the slice under it, bit 2 (4) is the slice under that, and so forth. So to turn the outer face and the slice under it would be the value 3 because 1 + 2 = 3.

I find this notation very intuitive and flexible even if the choice for the names (A-L in the case of dodecahedra) is sometimes a bit bland.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Wed Dec 14, 2011 5:58 pm 
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Konrad wrote:
I think that only five people have contriuted here.

Yes, but many more are reading it. Some (like me) just don't understand it all. We're waiting for the final committe decision, so we can get our heads around it.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Thu Dec 15, 2011 12:59 pm 
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I can write a final post with everything included, if that is OK.
I can do that probably tomorrow, because we have a family event tonight. :D
Everybody is invited to do a review and I would just edit the post if necessary.
When it is finished I'll provide a downloadable pdf as well.

I think a few synonyms will not hurt like U'2 = U2' or u = E = #2U.
(We will not have M or S slices, though)

I would use some pictures of the Starminx and a Teraminx (for moves like #3R)

Yes, U'2 is Gelatinbrain influenced and I think Brandon is right that it is quite logical.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Thu Dec 15, 2011 6:13 pm 
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While I see the merits of Andreas's face naming scheme for the dodecahedron, I prefer Konrad's scheme, for the same reasons he mentioned.

Image

If we remember that L and R are really FL and FR where we choose to leave out the F for convenience, opposite faces are intuitive in this system, for example, Front Right is opposite Back Left. I independently adopted exactly the same naming scheme in 2008 and it can be seen in some of my old posts in the Gelatinbrain thread.


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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Fri Dec 16, 2011 2:26 pm 
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Julian wrote:
While I see the merits of Andreas's face naming scheme for the dodecahedron, I prefer Konrad's scheme, for the same reasons he mentioned.
....
Thank you Julian for your support. I take it as a good sign that you came up with the same Notation in 2008.

I want to put together the "Twisty Puzzle Dodecahedron Notation". We should name it this way and use TPD-Notation as a shortcut for it.
(Konrad's scheme does not do justice to the many contributions from Burgo and others.)

Motivation: When the very interesting mass-produced Face Turning Starminx became available, Andrea felt the need for a commonly used notation for face turning Dodecahedra like Megaminx, Gigaminx, Teraminx, Petaminx, Pyraminx Crystal, FT Starminx, Pentultimate.
The well known Gelatinbrain program uses 12 letters, which are short but not intuitive for a human being.

There is no standard colour scheme for dodecahedra. Not even the twelve colours themselves are standardized. (E.g. my mf8 Gigaminx from Mefferts has very nice coloured stickers but different from the latest mf8 dodecahedra.)
When putting stickers to a dodecahedron, people could try to follow Gelatinbrain as closely as possible or follow the Crazy Megaminx scheme.
Personally I use something close to Gelatinbrain but some sticker colours from mf8 cannot be mapped. E.g. on Gelatinbrain there is no grey. When using colours in a text you should better provide a picture explaining your specific colour scheme. The diagrams below are all made by the usage of the Gelatinbrain program.

Here is the comparison of the Gelatinbrain notation and the result of the discussion above (In the diagrams you see the FT Starminx frontview /backview):

Image

1. Face names

We view the Dodecahedron sitting on a table and one face looking at us which we call F (front).
U (up) is on top and the opposite face on the table is D (down).
R (right) is the visible face at our right hand in the upper part.
L (left) is the visible face at our left hand in the upper part.
B (back) is opposite to F.
For the remaining 6 faces we use two letters:
DR (down right)
DL (down left)
UR (up right)
UL (up left)
BR (back right)
BL (back left)

In the following front view diagram I indicate the invisible faces via arrows.
Image

The B face cannot be shown here.

2. Outer face moves

As in WCA cube notation face letters are used for clockwise turns of outer faces.
U, D, F, B, L, R, DR, DL, UR, UL, BR, BL are single, clockwise turns by 72 degrees of the outer face layer.

The suffix ´ is used for anticlockwise turns:
U´, D´, F´, B´, L´, R´, DR´, DL´, UR´, UL´, BR´, BL´

the suffix 2 is used as a shortcut for two single clockwise turns:
U2, D2, F2, B2, L2, R2, DR2, DL2, UR2, UL2, BR2, BL2

The two suffixes can be combined in two ways(these are synonyms):
U´2, D´2, F´2, B´2, L´2, R´2, DR´2, DL´2, UR´2, UL´2, BR´2, BL´2
or
U2´, D2´, F2´, B2´, L2´, R2´, DR2´, DL2´, UR2´, UL2´, BR2´, BL2´

Note that on a cube U2 and U'2 are identical, but this is NOT true on face turning dodecahedras.
We can write for three single clockwise turns U3, R3 etc. Note that the result for U3 and U'2 is identical.

3. Inner slice moves

We follow the WCA notation for big cubes and use face names in lower case letters denoting an inner slice (inner layer) below an outer face.
u, d, f, b, l, r, dr, dl, ur, ul, br, bl are clockwise turns in the same direction as the respective outer face turns.

This photo shows the turn r halfway completed:
Image

We combine the suffixes ´ and 2 in the same way as above.

For dodecahedra with more layers like the Teraminx we need an additional notation. (This is missing in the WCA notation for big cubes).
We use the prefix `#` and the number of the layer combined with the face name to denote an inner layer turn:
e.g. `#3U` stands for `layer number 3 on the U face`

We allow #2 combined with the face name as synonyms for the lower case letter notation
e.g. #2U is equal to u.

It can be convenient to turn and write two or more adjacent layers together.
In WCA notation 2U is identical to U,u.
Therefore, we allow a number prefix without the # character denoting the number of layers turned together.
To make this a bit clearer we add the character `*`.
E.g. 3*U is identical to U, u, #3U and 3*U is a synonym for 3U (3*U seems better!)

4. Examples for different turns on different Dodecahedra

Image

5. Axis turns of the whole Dodecahedron

We write A(X) for a clockwise turn of the whole puzzle (A = All pieces) around an axis standing vertical on the centre of face X, where X is one of { U, D, F, B, L, R, DR, DL, UR, UL, BR, BL}
Respectivle A'(X) is an anticlockwise turn of the whole Dodecahedron.

y is a synonym for A(U) and y´ for A´(U)

6. Names for single pieces

As the many variants of FT Dodecahedra have various piece types, we cannot generalize the piece names.
Very often a piece can be described by combining face or inner layer names.
Edges can be named using the two faces they are in, corners the three faces they are in.
Because face names have either one or two letters we will use a hyphen to separate the face names e.g. U-UL for an edge or U-R-F for a corner.

For pieces that are only on a single face (one sticker only) we apply the rule that the face name is written first followed by further classification if there are more than one pieces of this type on a face.
E.g. `centre U` on a Megaminx is fully sufficient but for a startip on a FT Starminx you have to write U-R-F to name the startip on face U adjacent to corner U-R-F

Here follow some examples:
Image

EDIT: Thank you for the feedback, especially for some corrections by Burgo's PM! I have added the chapter about piece names following Burgo's suggestion.
Yesterday, I was probably in a hurry starting my Multidodecahedron assembly :lol:

EDIT2: Added a comment about different colour schemes in the Motivation paragraph.

EDIT3: I want to repeat the link to Brandon's script:
http://www.brandonenright.net/cgi-bin/gb_util.pl
The script translates Gelatinbrain to either Gelatinbrain (comments are extracted) or TPD Notation.

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Last edited by Konrad on Sun Dec 18, 2011 5:47 pm, edited 5 times in total.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Fri Dec 16, 2011 6:51 pm 
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Konrad,

Thanks very much for putting this together. It's very clear, easy to understand and pretty comprehensive. Much appreciated. :)

The only minor thing is under face names, you wrote "L (right)" where i think you mean left.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Sat Dec 17, 2011 5:42 am 
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Hi Konrad,

thank you for the great work. It is good understandable, I think.

Cheers,
Andrea


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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Sat Dec 17, 2011 9:02 am 
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I have made a few updates in my post above and have integrated the feedback I got so far.

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 Post subject: Re: Notation For Dodecahedron Puzzles
PostPosted: Sun Dec 18, 2011 4:56 am 
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This double post wants to draw your attention to text and pictures above in pdf file.
I hope it is good for something.
Feel free to use it wherever you want!

EDIT: I updated the pdf file.
It includes now a reference to Brandon's Sequence Utility at the end.


Attachments:
Twisty Puzzle Dodecahedron Notation2.pdf [684.43 KiB]
Downloaded 109 times

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