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 Post subject: Solving the Dayan Gem V
PostPosted: Tue Aug 13, 2013 2:44 pm 
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Finally had a chance to sit down and play with the Dayan Gem V today. Very neat little puzzle! I found it very confusing at first - just figuring out the color scheme was a challenge! I did manage to solve it after about 2 hours. Basically, I used sequences and ideas from the Vulcano [and therefore the Pyraminx as well]. A rough outline of my strategy is in white text below.


1. Solve the big-triangle faces. This involves figuring out the color scheme but is otherwise easy.

2. Now treat the puzzle as a Vulcano. Deep faces on the Gem V are Pyraminx-like turns on the Vulcano. Shallow faces turns on the Gem V are the face turns on the Vulcano. This allows us to equate Gem V rectangles with Vulcano edges.

3. Using Vulcano techniques, pair up all the rectangles.

4. At this point, only deep turns should be necessary. Solve like a Jing's Pyraminx. I have yet to encounter any parities.


I'm sure this is a bit unorthodox and probably not the most elegant, so I'd love to hear some other approaches. Thoughts?

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Aug 19, 2013 1:24 pm 
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I've been working on simplifying my method. It's actually much a simpler puzzle than I made it out to be. No need for translating sequences from the Vulcano this time! [That was confusing as heck.]

Notation: Hold shallow faces at U and F. Deep faces at L, R, D, and B. A square face should be staring at you. The shallow faces on the back side are simply l and r. Trapezoid pieces are "corners." Rectangles "edges" and are identified with two letters but ORDER IS IMPORTANT. UF would be the rectangle in the U layer adjacent to the F layer. FU would be the rectangle in the F layer adjacent to the U layer.

Method and explicit sequences in white text below.


1. Solve the corners. Again, requires knowing the color scheme but is fairly intuitive.
2. A clean 3-cycle of rectangles can be done as follows:

Cycle edges Ur-rU-rF: (R'LRL' BL'B'L) r (R'LRL' BL'B'L) r'
Cycle edges Ul-lU-lF: (R'LRL' BL'B'L) l' (R'LRL' BL'B'L) l

Think of the puzzle as a pyraminx. The square faces function as the edges. The parentheses part is a sequence that flips two edges. One piece is replaced with another by doing r. The squares faces are then flipped again and the replacement is undone. Since the edge flip is it's own inverse, this is fairly easy to remember. Edge flip, r, edge flip, r'. Simple! The mirror version is easy, too. Edge flip, l, edge flip, l'.

As performing B moves is awkward, an easier way to think of the part in parentheses is [R'LRL'], rotate puzzle 120 degrees, [LR'L'R], rotate puzzle back. And since these are just commutators, they are easy to reverse. With simple setup moves, these can be adapted to cycle other pieces to suit your needs.

3. If necessary, solve the small triangle centers. You can perform a 2-2 swap on these by doing (R'LRL')x3. This swaps centers on U and F as well as swaps centers on l and r.


That's it! Easy! I'm sure this can be cleaned up a bit further so that it cycles edges on the FRONT of the puzzle rather than the back [which is confusing], but this works and makes sense to me.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Sat Aug 24, 2013 8:20 pm 
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I used a similar method
1) solve corners, same way one would solve edges on an FTO or rex cube in an edges-first solve of those puzzles
2) pair up rectangles, creating squares (there are only 6 squares to make and if you get lucky and are a bit clever about planning ahead you can do two pairs at once, so this can be as few as 3 algorithms).
3) permute the squares (which act as edges) using a 3-cycle [R' L R L' (cw) or L R' L' R (ccw)] plus set-up moves.
4) swap centers same as themathkid's step 3 above

The only advice I would give for anyone starting out on this puzzle is to write down the color scheme first otherwise you end up in a big mess.

EDIT: five minutes after posting this i am now unable to solve the Dayan Gem V. I must have gotten a few fortuitious scrambles because this method isn't working for me at all now! Oh well I'll have to work on it some more :)

EDIT2: OK figured it out. One, when solving corners, you have to make sure the centers are in the correct places. This is similar to how on the Master Skewb, some solving methods suggest "checking for parity" for the centers before proceeding. If you build the corners correctly in relation to the centers then you avoid the situation where 1 center is solved and the other three need a 3-cycle (which as far as I know cant be done on this type of puzzle). The method used on the Dayan Gem IV as excellently tutorialized in video by Mr. rline here works great, except make sure you permute the corners as you go!. Two, sometimes the edge piece series in step 3 fails if the last two "squares" are paired, uh, not sure how to explain this, but in the wrong way. They need to be swapped with each other which you can't do using EPS. Just re-form the pair in the other orientation (using the 3 cycle for rectangles above or a similar method) and it falls into place. :)


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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Fri Sep 06, 2013 4:17 pm 
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I have the Gem V stickerless v1. My strategy is to start by building the square faces by moving rectangles to the thin strips they go with. No algorithms are necessary for the first 3 squares. For the last 3 one or two EPS and you're done.

Next I check the positions of the large triangles relative to the small ones. If all the triangles are solved, or if a double swap is needed, great! Go on to use EPS to place the squares in their correct positions relative to the small triangles. If 3 of the large triangles needed to cycle first, do the necessary twist, and then permute the squares with EPS.

If any of the squares need flipped so the trapezoids match up with their respective triangle centers, flip them.

If necessary, do a double swap of large triangles using Triple-EPS.

Finally use a commutator to place all the corner pieces. By now the colors are well established on the puzzle and it is easy to see what goes where. In fact using this method, the colors come together in a natural, easy way that makes it rather nice.

I have been attempting to make videos showing this process in detail. Ha! I have a whole new appreciation for rline, redkb, crazybadcuber, petethegeek, and all the others who take the time to make tutorials and walkthroughs. After several messups and restarts, I've decided to just outline my method above and leave it at that! :oops: :lol: :roll:

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Sat Sep 07, 2013 4:50 am 
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I don't know why rline has not posted a link to his Gem V tutorial in this topic.
Maybe, he is so busy making new videos that he has no time left to post about them? :lol:

I think it is a great tutorial.

I own Timur's F-Skewb and somebody pointed out already that F-Skewb and Gem V are almost logically identical.
So, it was no surprise that I could solve the Gem V following my methods for the F-Skewb.
I think the colour scheme and the shape makes the Gem V a bit trickier.
rline's tutorial lets look it quite simple.

BTW, I'm sure that most if not all of rline's tutorials are good. I just do not have the time to look at all of them. I don't know how he and other "hard liners" (meaning people who contribute so much to the twisty puzzle community) manage a normal life :) (My wife considers me a "hard liner" myself and I cannot spend more time for TP without risking divorce :lol: )

EDIT: I had a look at the other posts in this thread and made the following interesting observation.
themathkid has introduced in his hidden spoiler the same notation as the one I came up with. (At least I guess it is the same, because he has not explained it in detail.)
I was influenced by the F-Skewb and other vertex turning cubes (e.g. the Master Skewb).

rline has introduced a different notation when he explained how he uses the "Corner Piece series) for edges 3-cycles. rline's notation fits better for describing the [3,1] commutator he is using.

BTW, I use a variety of [3,1] commutators for the large edges and a [4,1] for swapping the small triangles.
I could use a [3,1] for the small edges (corners), but I do not need it.

Another observation: Everybody (rline and this thread) talks about "corners" where I would describe "small edges" (the others as large edges).
They are "edges" on the F-Skewb shape mod for sure :) . (The little centre triangles are the 4 corners of the F-Skewb, while the large triangles are hidden on the F-Skewb.)
Personally, I would name pieces between two faces always as edges.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Sat Sep 07, 2013 7:36 pm 
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Konrad wrote:
I don't know why rline has not posted a link to his Gem V tutorial in this topic.
Maybe, he is so busy making new videos that he has no time left to post about them? :lol:

I think it is a great tutorial.
I too enjoyed working through rline's tutorial, although, of course, the method I came up with makes more sense to me. :D

Konrad wrote:
I own Timur's F-Skewb and somebody pointed out already that F-Skewb and Gem V are almost logically identical.
So, it was no surprise that I could solve the Gem V following my methods for the F-Skewb.
Isn't it funny how this works? Somewhere online someone said they thought Gem V was like Vulcano! I don't see it myself. To me the Gem V is like a Jing's Pyraminx. I have made an 8 and a half minute video pointing out the similarities.
Konrad wrote:
I think the colour scheme and the shape makes the Gem V a bit trickier.
I love the colour scheme of the stickerless v1 Gem V. It is so much like a standard Rubik's Cube!

Konrad wrote:
BTW, I'm sure that most if not all of rline's tutorials are good. I just do not have the time to look at all of them. I don't know how he and other "hard liners" (meaning people who contribute so much to the twisty puzzle community) manage a normal life :) (My wife considers me a "hard liner" myself and I cannot spend more time for TP without risking divorce :lol: )
rline amazes me too. Family, job, and all the time he puts in on twisty puzzles! But Konrad, really—I for one, and most here would agree, that you are one of the hard liners, for sure. :D

Konrad wrote:
Personally, I would name pieces between two faces always as edges.
On the Gem V, the little edges around the big triangle—I think of those 4 pieces taken together as a corner. Do you know how to use Triple-EPS on a Jing's Pyraminx to do a double swap of corners? You can do exactly the same thing on the Gem V. So although I can see your point of calling them edges, it also makes sense to me to call them corners.

Perhaps after a dozen or so more solves, I will try again to make a video showing my technique, which I briefly described above a couple posts back.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Sun Sep 08, 2013 5:17 am 
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robertpauljr wrote:
...I too enjoyed working through rline's tutorial, although, of course, the method I came up with makes more sense to me. :D
.....
Naturally :)
On the other hand, your method seems to fit with the sticker less version. On the versions with one colour bodies and stickers we have got no "stripe" pieces to be solved.

EDIT:

I have now tried robertpauljr's outline and solved it his way.
robertpauljr wrote:
...Next I check the positions of the large triangles relative to the small ones. If all the triangles are solved, or if a double swap is needed, great! Go on to use EPS to place the squares in their correct positions relative to the small triangles. If 3 of the large triangles needed to cycle first, do the necessary twist, and then permute the squares with EPS. ...
I guess that you need more to memorize about the colour scheme than with rline's method. How else can you check the position of the triangles early in the game?
Also, you need to cover the special case when all triangles are on place but two sets of composed edges need to be swapped. (A 2-2 swap of large edges which can be done by two pure 3-cycles.)

What commutator are you using for the corners (small edges)? I have a [3,1] that involves inner slice turns.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Sun Sep 08, 2013 8:27 pm 
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Rline's tutorial really helped me and took me from being confused to solving my DaYan Gem V in one viewing (and a couple of rewinds). No new algorithms. In fact, once I got the idea I was able to work ahead in a couple of places.

For the stickerless version, I take it that there is a coloured "stripe" (thin edge) between the rectangular edge pairs? This would make it more like a "Super Gem V". Isn't this a substantial change over the regular solve?

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Sun Sep 08, 2013 9:13 pm 
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Konrad wrote:
I guess that you need more to memorize about the colour scheme than with rline's method. How else can you check the position of the triangles early in the game?
Well, I started by memorizing that with the white square at the very top, little green is at the upper left, little yellow is at upper right, and little pink is at lower front. But really was it necessary to memorize? I think not. Because the more I played with it, I realized the little triangles are always solved relative to each other, just as the centers of a Rubik's cube are always solved relative to one another.

To check the positions of the big triangles, I had to memorize nothing new, because I already know the standard color scheme of a Rubik's Cube and this puzzle is the same! Big blue is opposite little green. And so forth.

Konrad wrote:
What commutator are you using for the corners (small edges)? I have a [3,1] that involves inner slice turns.
To answer this I will either have to make a video showing them, or learn some sort of notation. I'll get back to you later on this.

Pete the Geek wrote:
Rline's tutorial really helped me and took me from being confused to solving my DaYan Gem V in one viewing (and a couple of rewinds). No new algorithms. In fact, once I got the idea I was able to work ahead in a couple of places.
Nice. Do you have a Jing's Pyraminx? Did you watch the video I posted? Do you see the similarities?

Pete the Geek wrote:
For the stickerless version, I take it that there is a coloured "stripe" (thin edge) between the rectangular edge pairs? This would make it more like a "Super Gem V". Isn't this a substantial change over the regular solve?
I only have the stickerless version with the thin stripes down the middle of the square faces. When building the square faces at the beginning of my solve, if the stripes were not there, instead of moving two rectangles to the stripe, I would just move the two rectangles together anywhere. It seems to me that would be substantially easier, but that is just my opinion.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Sun Sep 08, 2013 9:30 pm 
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Pete the Geek wrote:
Rline's tutorial really helped me and took me from being confused to solving my DaYan Gem V in one viewing (and a couple of rewinds). No new algorithms. In fact, once I got the idea I was able to work ahead in a couple of places.

For the stickerless version, I take it that there is a coloured "stripe" (thin edge) between the rectangular edge pairs? This would make it more like a "Super Gem V". Isn't this a substantial change over the regular solve?

I had a rant in my unboxing video saying that the colourless version 1 was only different to the black version via colour scheme. Now, I will concede that the stripes on the coloured version do change the solve. But the stripes weren't a deliberate ploy by the company to make a more interesting solve. They're just what result with the coloured plastic. On the black version all the stripes are black so it's simple.

The only difference to the solve that I would make (using my method) is that instead of just pairing up the rectangles anywhere using the CPS, I would place the rectangles straight onto their correct stripe. At the end of that, the squares would either be correctly in place, or else flipped.

So in my opinion it is a change from the regular solve, but not substantial.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Sun Sep 08, 2013 9:38 pm 
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rline wrote:
So in my opinion it is a change from the regular solve, but not substantial.

So there you have it, Pete, rline says it is not substantial. I like to think of it as substantial. :lol: :lol: :lol:

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Sun Sep 08, 2013 9:44 pm 
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robertpauljr wrote:
rline wrote:
So in my opinion it is a change from the regular solve, but not substantial.

So there you have it, Pete, rline says it is not substantial. I like to think of it as substantial. :lol: :lol: :lol:

rline says that in his opinion it is not substantial :)

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Sep 09, 2013 12:42 am 
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Konrad wrote:
I have now tried robertpauljr's outline and solved it his way. (snip) Also, you need to cover the special case when all triangles are on place but two sets of composed edges need to be swapped. (A 2-2 swap of large edges which can be done by two pure 3-cycles.)
Once the composed edges are built, and the triangles are checked, all you need is several applications of the 4 move EPS to get the composed edges—made up of two large rectangle edges and the stripe between them—into place. Corners—small edges—get moved around at this point too, but I don't care since I solve them last.

I don't know if I have spelled this out before, or if it was in one of the videos I gave up on, but when I am using EPS to place the composed edges, I either use small triangles as the center of rotation, or if it works out that it seems easier to use large triangles, instead of going from piece 1 to 2 to 3, I go 3 to 2 to 1 and do it twice, or in other words a double EPS. This is so the small triangles stay solved in relation to the composed edges that are being placed between them.

Now some people will want to orient the composed edges as they permute them. This is good. At this point, I haven't wanted to put in the extra thought required. Just slam the squares home, then flip pairs of them after they are all permuted. I have two different edge flipping techniques which I use on lots of different puzzles. One is to do one EPS using the 2 composed edges as pieces 1 and 3, then use another EPS to put the three pieces back home oriented correctly.

Konrad wrote:
What commutator are you using for the corners (small edges)? I have a [3,1] that involves inner slice turns.
Video demonstration of the commutators

Basically the commutator is this:

Move a piece from the middle slice to the top layer.
Replace the piece with a piece on the top layer.
Move that piece from the top to the middle slice by undoing the first twist.
Replace it with a twist of the middle slice.
Move it back up.
Undo the first move of the top layer.
Move it back down.
Undo the first move of the middle layer.

If no setup moves are used, it is a pure 3-cycle of 2 pieces on the middle layer slice, and one on either the top or bottom layer, depending on which way you twist the top layer.

rline wrote:
rline says that in his opinion it is not substantial :)
:D One thing I've learned through this twisty puzzle obsession is that different puzzlers have different ways of seeing things, and methods that click with one person may seem overly difficult to another. I enjoy rline's videos! We have worked through various puzzles together over the years. Sometimes I see what he does and think, Wha?! Why go to all that bother? But sometimes I see what he does and think, Wow! That's brilliant! And I laugh at myself for making something so difficult that he does so elegantly.

rline, here is something to think about: If the Gem V had been around early in your puzzling career, you may have come up with my method. Why? Because it uses simple moves and EPS to solve edges first, then finishes by solving "corners" last with an 8 move commutator. It is a lot like the Ultimate Solution that you mastered and applied to many puzzles in your early days of puzzling. :D

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Sep 09, 2013 3:17 am 
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robertpauljr wrote:
rline, here is something to think about: If the Gem V had been around early in your puzzling career, you may have come up with my method. Why? Because it uses simple moves and EPS to solve edges first, then finishes by solving "corners" last with an 8 move commutator. It is a lot like the Ultimate Solution that you mastered and applied to many puzzles in your early days of puzzling. :D

I personally only use the Ultimate solution when I can't seem to adapt my beginners techniques to a puzzle and then the ultimate solution is effectively down to the absolute basics. So when I solved this I did it the same way as Rline and only had to use his video when I couldn't work out how to swap 2 pairs of centres! :oops:

To me it looks like you both used the ultimate solution but one of you relied more on EPS and the other more on CPS to move different pieces around. I like the two approaches because it shows how using very basic techniques can achieve similar ends. Robert's technique requires finding an 8 move commutator and, whilst I understand them, I still can't find them myself unless they leap out at me! I'm just not bright enough to be able to work them out (especially on a scrambled puzzle!)

Why did I choose Rline's method? Because I couldn't work out what to do with the "corners" so felt it safest to place them first and then move everything else whilst leaving them intact!

I always find these conversations fascinating - its like being on the sidelines of a conversation between geniuses! I understand a few words in each sentence and that gives me a warm glow! :shock:

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Sep 09, 2013 10:54 am 
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Puzzlemad wrote:
Robert's technique requires finding an 8 move commutator and, whilst I understand them, I still can't find them myself unless they leap out at me! I'm just not bright enough to be able to work them out (especially on a scrambled puzzle!)

Kevin, some people like to scramble their puzzles immediately when they get them, and then work out a solution. I do not! Much of the fun of puzzle solving for me is the pre-initial-scramble analysis in which I specifically look for commutators. I don't always do a thorough enough job of it. Sometimes I just get antsy to scramble it and go for it. Sometimes I lose track of what I am doing and accidentally scramble it.

If you are up for a mini-tutorial on commutators, here you go—

On a solved Rubik's cube, do RUR'. Look at the top layer. 6 of the 8 pieces are affected. Ugh.

But on the middle layer (the layer between U and D) only 1 edge is affected. That is the kind of thing I look for when looking for commutators. Since only 1 edge is affected, you can replace the affected edge with any of the 3 other edges in the middle layer. Try it. Then do RU'R', which undoes the initial RUR'. Then undo the middle layer twist you did. You just 3-cycled edges!

Now you can take it a step further. The edge in the middle layer that got replaced by your initial RUR' was at FR. You replaced it with the edge at UB. That is because of the U in RUR'. What if you had done RU'R' initially? It would replace it with UF instead. What if you had done RU2R' instead? It would replace it with UL instead.

In other words, you can cycle FR to any of the other 3 spots in the middle layer to any of 3 spots in the top layer. So on a 3x3x3 cube that is the equivalent of 9 different algorithms for 9 different scenarios. But you don't have to remember 9 different cases, or 9 algorithms. You just focus on the three pieces you want to cycle and do a series of replacements, like this:

1. Move FR up. R
2. Replace it with the edge on top you want to cycle to FR. U or U' or U2
3. Move the new FR down. R'
4. Replace it with the edge in the middle layer you want to cycle to the top. E or E' or E2
5. Move it up. R
6. Undo step 2. U' or U or U2
7. Move it down. R'
8. Undo step 4. E' or E or E2

Furthermore, when you do RUR' on a solved 3x3x3 cube, you'll notice that only one corner in the bottom layer is affected. That means you can 3-cycle corners the same way! For example, RUR' D RU'R' D'. Try it with different combinations of U and D, like RU2R' D2 RU2R' D2.

Get this and you are well on your way to finding your own commutators for the Gem V and countless other puzzles. :D

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Sep 09, 2013 3:44 pm 
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Thank you so much for going through that! I really appreciate it. I must say that I finally understand the idea behind commutators! With help from Jon (SuperAntonioVivaldi), Rline, Burgo and Brandon I really do understand the basics of them. BUT finding them myself is a much harder proposition which I have only done once myself (on the Starminx). Plus what you describe on a cube is easy but on a more complex puzzle quickly becomes incomprehensible to me! :shock:

I also would like to investigate a puzzle myself before scrambling but almost every single time I end up with a mess and then I'm stuck with a scrambled puzzle to solve. I sometimes try using gelatinbrain but struggle to convert the 2D images to 3D (despite having no trouble interpreting CT and MRI scans).

I was lucky with the gem V that I managed to work out what an eps and cps did before I lost control and scrambled it!

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Sep 09, 2013 4:30 pm 
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Puzzlemad wrote:
Thank you so much for going through that!
Gladly!

Puzzlemad wrote:
I also would like to investigate a puzzle myself before scrambling but almost every single time I end up with a mess and then I'm stuck with a scrambled puzzle to solve.
Many times I resort to taking a puzzle apart and reassembling it solved, but as the puzzle hardware gets more complex, this becomes less of an alternative. :(

Puzzlemad wrote:
I sometimes try using gelatinbrain but struggle to convert the 2D images to 3D (despite having no trouble interpreting CT and MRI scans).
I was introduced to CT and MRI images last fall, when I had a substantial tumor removed. Very amazing technology. So you get to do this for a living? Nice!

Quote:
I was lucky with the gem V that I managed to work out what an eps and cps did before I lost control and scrambled it!
I hear ya! :lol:

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Sep 09, 2013 4:52 pm 
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robertpauljr wrote:
I was introduced to CT and MRI images last fall, when I had a substantial tumor removed. Very amazing technology. So you get to do this for a living? Nice!

I'm very sorry to hear that! I hope it was curative surgery!
I am a consultant anaesthetist in a major UK teaching hospital - sort of the equivalent of an Attending physician anesthesiologist in one of the major university hospitals in the US. I don't view CTs and MRIs as a profession but have to look at them regularly for patients I will have to anaesthetise for major surgery. It's fun and pays for a lot of puzzles! :lol: :lol: :lol:

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Tue Sep 10, 2013 11:24 am 
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robertpauljr wrote:
...
Konrad wrote:
What commutator are you using for the corners (small edges)? I have a [3,1] that involves inner slice turns.
Video demonstration of the commutators

Basically the commutator is this:

Move a piece from the middle slice to the top layer.
Replace the piece with a piece on the top layer.
Move that piece from the top to the middle slice by undoing the first twist.
Replace it with a twist of the middle slice.
Move it back up.
Undo the first move of the top layer.
Move it back down.
Undo the first move of the middle layer.

...
As it happens this is the very same commutator ( + variants) I would use for (pure) 3-cycles of small edges (corners). I have explained it for other puzzles like the Master Skewb before.
(Actually I do not need it for the Gem V at all)

As you can see, it is not so easy to explain an eight turn commutator verbally :wink: .
So, let me show the notation I'm using (and as I guess is the same used by themathkid in his spoiler in his second post on top of this topic).
It is the same I'm using for the F-Skewb. Therefore I show the two in one diagram:
Image
The commutator above translates to r U r' u r U' r' u' = shortcut [[r:U],u] a [[1:1],1] or [3,1] commutator.

The notation of inner slice moves are lower case letters describing the layer beneath the upper case outer face (vertex on the F-Skewb).
Because we have eight faces (eight vertices) on the Gem V (F-Skewb) and six letters only in the (Singmaster) 3x3x3 notation, I have added DBR (= DRB = Down Right Back vertex) and DFL for completeness. I never need these three letter turns.

In my opinion it is OK to say that the F-Skewb and the Gem V are (almost) logically equivalent puzzles.
If you make the inner pieces under the corners R, L, D, B in my diagram distinguishable they become the equivalent of the large triangles on the Gem V and you can say that they are logically completely identical.

The comparison with the Jing's Pyraminx I would rephrase to "Reduce the Gem V to a Jing's Pyraminx."
The tedious part of robertpauljr's method is obviously the permutation of the small edges (corners).
This is done by 8 move commutators where 6 of them are inner layer moves.
Inner layer moves are a bit more cumbersome than outer layer moves on this physical puzzle.
So, my vote is clearly for a method where the small edges (corners) are done in an intuitive way first and the large edges are grouped by outer layer moves i.e. pure 3-cycles by adapting the Corner Piece Series to the Gem V.
My own large edges 3-cycle r L R' L' r' L R L' = [r,[L:R']] involved two inner layer turns, so, I would vote for the pure outer layer CPS from rline. If you look at his tutorial, be warned that his notation is different from the one in the diagram above. It makes perfect sense for his purpose, though.

BTW, as I said, I guess that themathkid uses the same notation in his hidden spoiler. If this is true the "commutators" in themathkid's spoiler have to be corrected
themathkid wrote:
...Cycle edges Ur-rU-rF: (R'LRL' BL'B'L) r (R'LRL' BL'B'L) r'
Cycle edges Ul-lU-lF: (R'LRL' BL'B'L) l' (R'LRL' BL'B'L) l

....
As you probably remember a commutator is usually written in a generic form as X, Y, X' Y'
The X part in the spoiler is (R'LRL' BL'B'L) and Y is r, therefore the second term in brackets should be X'= (L'BLB' LR'L'R) and the whole sequence becomes an [8,1] commutator.
I wrote this comment in a PM to themathkid but got no reply and he has not corrected his post either.
Therefore, I wanted to give this hint here, openly.
(Maybe, nobody bothers anyway, because 18 moves are 10 moves more than 8? :wink: )

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Tue Sep 10, 2013 1:24 pm 
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Konrad wrote:
...As it happens this is the very same commutator ( + variants) I would use for (pure) 3-cycles of small edges (corners). I have explained it for other puzzles like the Master Skewb before.
(Actually I do not need it for the Gem V at all)
Good to hear you are familiar with it. I sort of figured that anyone, like you, who is good at coming up with commutators, would see that what I am using is just a simple basic [3,1] commutator that uses two parallel layers and one layer that intersects both, which is used to interchange the 3 pieces in the parallel layers.

Konrad wrote:
As you can see, it is not so easy to explain an eight turn commutator verbally :wink: .
That's for sure! :lol:
Konrad wrote:
So, let me show the notation I'm using (and as I guess is the same used by themathkid in his spoiler in his second post on top of this topic).
Thank you for this. It makes sense to me, especially with your diagrams. One interesting thing I notice, is that your color scheme is slightly different than mine. Did you notice that when you watched my video?

Konrad wrote:
The commutator above translates to r U r' u r U' r' u' = shortcut [[r:U],u] a [[1:1],1] or [3,1] commutator.
Technically, yes, but in practice I only do 2 inner slices in carrying it out. Two! Not Six! (Rr) U (Rr)' u (Rr) U' (Rr)' u'. And to do u I do Uu U', and frequently the final U' is cancelled by a setup move.

Konrad wrote:
The comparison with the Jing's Pyraminx I would rephrase to "Reduce the Gem V to a Jing's Pyraminx."
I agree that a Gem V can be reduced to a Jing's Pyraminx. When I was first working with the Gem V I was not looking for a logical equivalence. I just noticed a similarity, which just gave me a good starting point to work from when deciding how to approach it. Honestly, I do not think of the Jing's Pyraminx any more as I solve the Gem V. I just think of the Gem V. :D
Konrad wrote:
The tedious part of robertpauljr's method is obviously the permutation of the small edges (corners).
I agree that solving the small edges (corners) is the most tedious part of my method, but usually I can permute 2 pieces at once, and it all goes rather quickly.
Konrad wrote:
This is done by 8 move commutators where 6 of them are inner layer moves. Inner layer moves are a bit more cumbersome than outer layer moves on this physical puzzle.
As explained above, in practice, this is not correct. There are only 2 inner layer moves.

Konrad wrote:
So, my vote is clearly for a method where the small edges (corners) are done in an intuitive way first and the large edges are grouped by outer layer moves i.e. pure 3-cycles by adapting the Corner Piece Series to the Gem V.
This is fine, and makes sense, but I, for one, find it much easier to quickly identify what goes where with my method. There is just something confusing to me that really slows me down and makes for mistakes when I am not matching pieces up with centers. I wanted to present my method for others that may be struggling with the same thing.

Konrad wrote:
My own large edges 3-cycle r L R' L' r' L R L' = [r,[L:R']] involved two inner layer turns, so, I would vote for the pure outer layer CPS from rline. If you look at his tutorial, be warned that his notation is different from the one in the diagram above. It makes perfect sense for his purpose, though.
It has been awhile since I have watched rline's tutorial. How would his 3-cycle translate into your notation?

Thanks for the feedback, Konrad. I think it is good to share pros and cons of different solving methods.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Tue Sep 10, 2013 5:15 pm 
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robertpauljr wrote:
...Technically, yes, but in practice I only do 2 inner slices in carrying it out. Two! Not Six! (Rr) U (Rr)' u (Rr) U' (Rr)' u'. And to do u I do Uu U', and frequently the final U' is cancelled by a setup move.
I understand what you mean. Fair enough.
The notation does not correspond to my notation, though.
You would need small triangle faces at U and R.
robertpauljr wrote:
...It has been awhile since I have watched rline's tutorial. How would his 3-cycle translate into your notation?
...
I hope this picture explains it good enough.
Image
Rline's notation uses three names only, so, I show the result on a solved Gem V by adding one changed layer in the right part of the image.
The whole puzzle is turned in space from the left part to the right part that the former (blue face) B layer on the left becomes U on the right.
In my notation DLF is the thin layer opposite to R, in rline's it is simply L opposite to R.

I guess you understand why I said before that rline's notation makes complete sense for the CPS sequence.
You can make up several variants of this by mirroring, reversing and changing the direction of moves.
E.g. (rline's notation) R U L' U' R' U L U'

BTW, the colour scheme is my own. I got a purple body unstickered.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Tue Sep 10, 2013 9:49 pm 
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Konrad wrote:
BTW, the colour scheme is my own. I got a purple body unstickered.

Thanks for the clarification. :D

OK, I've done several 3-cycles of big edges now and I have to admit, it is far easier than cycling little edges! I hold a small triangle on U or D and a large triangle on R, and do any one of the following depending on where the pieces are that need to cycle:

(R U R') D (R U' R') D'

(R U' R') D (R U R') D'

(R U R') D' (R U' R') D

(R U' R') D' (R U R') D

Am I convinced that I will like a method that does big edges last? Not yet, but I'm going to give it a try. :D

I need to see if I can work it out so I can establish the color scheme early in the solve without having to memorize where even the first few pieces go. And then I'll need to see how the center strips on the square faces work out with this method. And who knows what other challenges there will be along the way.

But I am hopeful.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Wed Sep 11, 2013 12:22 pm 
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robertpauljr wrote:
I need to see if I can work it out so I can establish the color scheme early in the solve ...

Got it! It is quite a bit different from rline's method, but thanks to rline and Konrad for convincing me there was possibly an easier way than using the [3,1] commutator with an inner slice involved.

1. Get all the centers—small triangles, large triangles, and if you have stickerless v1 as I do, the thin strips on the square faces. All 8 triangles can be solved with either 0, 1, or 4 moves. The 6 thin strips take me up to 3 Double-EPS, or 24 twists. I use Double-EPS to maintain centers.

2. Place all the small edges (corners) from the bottom up. Uses an Up-Replace-Down technique.

3. Use [3,1] commutators to solve the large edges.

That's it! :D :D :D

(edited)

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Sep 23, 2013 2:37 pm 
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I am left with 3 unsolved center pieces. How you can deal with that?


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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Sep 23, 2013 3:06 pm 
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doctor twist wrote:
I am left with 3 unsolved center pieces. How you can deal with that?

In my solution outlined directly above, I deal with all 8 of the triangle centers, and all 6 of the thin strip centers of the square faces in step 1, so that I never end up in the situation you describe of being left with 3 unsolved center pieces. My motto: Deal with parity as early as possible so you don't have to unsolve and re-solve at the end.

So, here is how I deal with the centers in a little more detail. Starting with a scrambled puzzle,

1. I hold the puzzle so there is a square face on top, and the large red triangle is on the upper half of the front, and the large purple triangle is on the upper half of the back. This is totally arbitrary, but it is what I am used to looking for and it defines for me the color scheme of the whole puzzle. (It is sort of like when I am solving a Rubik's Cube I start by holding it with the white center on the bottom.)

2. With the Red Triangle in front, I can see 3 small triangles. By looking at these 3 I can tell whether they are solved, or whether they need a double swap, or whether I need to do one twist that will solve them. If the one twist is required I do it. If the double swap is required I do it. (So I deal with the "3 unsolved center pieces" before anything else on the puzzle is solved!

3. Since I have the stickerless version, there are colorful thin strips on the square faces. I place them next using Double-EPS moves. I use Double-EPS instead of just EPS so that the 8 triangle centers don't scramble during this phase. So if I need to move thin strip A to thin strip B to thin strip C, I go the opposite way twice! C to B to A twice is the same as A to B to C, and with each EPS there is a double swap of center triangles, so doing it twice leaves them solved. :D

So that is how I deal with it. But what if someone handed me a puzzle with everything solved except for 3 triangle centers? Then what would I do? I would do a single twist that solved them, then re-solve the puzzle from there. What a pain! That is why I like to insure at the very beginning that this will not happen.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Sep 23, 2013 4:19 pm 
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doctor twist wrote:
I am left with 3 unsolved center pieces. How you can deal with that?

In my understanding of the puzzle, the only way around this is to twist them into position, and then re-solve the puzzle. As Robert says it's a pain. In my video, I specifically show when and how to put them into position so that this won't happen. Sure, it's possible to get a 2+2 swap of centers but that's simple to deal with.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Sep 23, 2013 4:44 pm 
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Thank you very much for the detailed explanation.

I asked myself if there is a simple alg to solve that parity??

I followed your advice and did one turn which solved the centers and then resolved the cube/ the gem.
It didnt take much time.

I guess it would take me longer if I would use your method. If I get you right you´re doing always two EPS instead of one, or? This takes some extra time too.

However it is really a fun puzzle :D


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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Sep 23, 2013 4:55 pm 
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rline wrote:
doctor twist wrote:
I am left with 3 unsolved center pieces. How you can deal with that?

In my understanding of the puzzle, the only way around this is to twist them into position, and then re-solve the puzzle. As Robert says it's a pain. In my video, I specifically show when and how to put them into position so that this won't happen. Sure, it's possible to get a 2+2 swap of centers but that's simple to deal with.


I love your tutorials!! They are really really fabulous!
Your solving strategy is very efficient. You´re just using simple EPS and avoid the double EPS to keep the centers intact. And you´re right, a 2+2 swap of centers in the end is not a big deal :-)


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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Sep 23, 2013 5:31 pm 
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doctor twist wrote:
Thank you very much for the detailed explanation.
Sure thing.

doctor twist wrote:
I guess it would take me longer if I would use your method. If I get you right you´re doing always two EPS instead of one, or? This takes some extra time too.

Let's clarify. No, I am not always doing 2 EPS instead of one. Only in one phase do I do that. Only when solving the colorful thin strips. This only happens two times usually. So I am doing 16 EPS twists instead of 8 EPS twists. But in doing the 8 extra twists I potentially avoid having to do a Triple-EPS later in the solve to double swap the triangle centers. So I do 8 extra twists early on that potentially eliminates 12 twists later.

In steps 2 and 3 I do not need to use EPS at all.

Here is the complete method.

1. Get all the centers—small triangles, large triangles, and if you have stickerless v1 as I do, the thin strips on the square faces. All 8 triangles can be solved with either 0, 1, or 4 moves. I do not mean each! I mean that after either 0, 1, or 4 twists all 8 triangles are solved!

The 6 thin strips take me up to 3 Double-EPS, or 24 twists. I use Double-EPS to maintain centers. Rarely it takes three of them. Rarely are they already solved. Usually it takes two Double-EPS to solve all 6 pieces.

2. Place all the small edges (corners) from the bottom up. Uses an Up-Replace-Down technique. Some people call this truncated EPS, since it is the first 3 twists of the EPS.

3. Use [3,1] commutators to solve the large edges.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Mon Sep 23, 2013 6:38 pm 
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doctor twist wrote:
I am left with 3 unsolved center pieces. How you can deal with that?


The small centers should be correctly positioned before working on the rectangles / large edges. This is an important part of figuring out the color scheme & solving the small edges. Luckily, they are pretty simple to position early on. A 2-2 swap is easy to do without disturbing the small edges [this is just like manipulating corners of a skewb / centers of a Jing's Pyraminx]. The only other scenario is the one you ran across - needing a 3-cycle. As rline suggested, a single deep turn will 3-cycle the centers, but then it becomes apparent that the small edges are incorrect, which means you probably goofed on getting the color scheme correct. Totally understandable, though - that's the most confusing part by far on this puzzle!

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Tue Sep 24, 2013 9:03 am 
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doctor twist wrote:
I am left with 3 unsolved center pieces. How you can deal with that?
I do not have to add much to the explanations above, just a little sequence, so it is no longer a pain or a problem. :)
My outline is identical to rline's tutorial:
A. Memorize colour scheme: just one face with large triangle centre and how it is surrounded by small edges (corners)

1. Start with the memorized centre and put all small edges (corners) to their correct positions. Take care of the large triangle centres, while you are doing this.
2. Check the small triangle centres: If they are correct or need a 2-2 swap go to step 3. Otherwise do the eight turns in my diagram. Please, recognize that it is the same than just doing one turn of the R-face (in my example) and solve the small edges again. Just that this move sequence preserves the small edges.
3. Solve the large edges (rectangles) by pure 3-cycles (& group two as in rline's tutorial)

My diagram shows the problem "small triangles need a 3-cycle" on a solved Gem V in the upper part.
Instead of just doing R and "solve it again", I use a sequence of 8 turns that preserves the small edges.
The result is a 3-cycle that is pure regarding small edges.

Image

The large edges would need another pure 3-cycle. Please remember that the "parity check" is done before any large edges are solved.

My opinion remains unchanged: This is easier for me than doing the little edges last. (I have ordered a full coloured version and check it again, when the "stripes" need to be solved too.)

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Tue Sep 24, 2013 10:30 am 
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Konrad wrote:
My diagram shows the problem "small triangles need a 3-cycle" on a solved Gem V in the upper part.
Instead of just doing R and "solve it again", I use a sequence of 8 turns that preserves the small edges.
The result is a 3-cycle that is pure regarding small edges.
I have tried this and it is very nice. Not only does it leave the small edges intact, but it only disrupts 3 of the large edges! Wow! Konrad, you have a very nice solution to doctor twist's question.

Konrad wrote:
The large edges would need another pure 3-cycle. Please remember that the "parity check" is done before any large edges are solved.
Konrad, why not check the small triangles in relation to the large triangles before solving the small edges in step 1? Then it would only require 1 twist, since there would be nothing to maintain.

Konrad wrote:
My opinion remains unchanged: This is easier for me than doing the little edges last. (I have ordered a full coloured version and check it again, when the "stripes" need to be solved too.)
I have the full colored version, and I have tried various approaches. In the method I first devised I solved the little edges last, but you convinced me to look for a way that did not require slice moves in the pure 3-cycle. And so I did. With the full coloured stickerless version I solve all 8 triangles first. This usually takes 1 twist to accomplish, but sometimes it requires 1 EPS. Then I solve the 6 stripes. (I have explained in the thread above in detail how I go about it and why.) Then I solve all the small edges. At this point, since all the triangle centers are solved it is easy to tell what goes where. Then I use pure 3-cycles to put the large edges home.

Yesterday I tried solving it several times without solving the stripes at all. I just pretended they were all black and ignored them. I found that the overall solve was both easier and harder. It was easier inthat I did not have to solve the stripes. But it was harder inthat I had to think more when solving the large edges about what goes where colorwise. With all the triangles and all the stripes solved at the very beginning it quickly establishes the color scheme, and makes for an easier solve along the way.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Tue Sep 24, 2013 2:17 pm 
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robertpauljr wrote:
...
Konrad wrote:
The large edges would need another pure 3-cycle. Please remember that the "parity check" is done before any large edges are solved.
Konrad, why not check the small triangles in relation to the large triangles before solving the small edges in step 1? Then it would only require 1 twist, since there would be nothing to maintain.
....
This would require much more memorizing of the colour scheme. As rline, I memorize a single face only. Instead I invest an eight move sequence in 50% of the cases :)

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Tue Sep 24, 2013 3:02 pm 
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Konrad wrote:
robertpauljr wrote:
...
Konrad wrote:
The large edges would need another pure 3-cycle. Please remember that the "parity check" is done before any large edges are solved.
Konrad, why not check the small triangles in relation to the large triangles before solving the small edges in step 1? Then it would only require 1 twist, since there would be nothing to maintain.
....
This would require much more memorizing of the colour scheme. As rline, I memorize a single face only. Instead I invest an eight move sequence in 50% of the cases :)

Yes, but once the color scheme is learned, and the stickerless v1 scheme is quite easy to learn, all subsequent solves are so much easier. It isn't just doing the 8 move sequence—it is learning and remembering the 8 move sequence. And I find it visually easier to solve a puzzle when I do not have to ignore unsolved centers later in the solve. When placing the large edges, it is nice having the 3 small edges matching the small triangle centers, so nothing has to be ignored at that point. It helps me keep from getting confused.

Another nice thing about solving all the centers first, is that you never have to remember when to think about the locations of the small triangles later in the solve. You know how part way through the solve you have to make sure they are either solved or double-swapped. This is an extra step you must take with every solve that I never have to remember to do.

I'm not saying your method is bad. It seems to be the most popular method from the feedback given. I'm just saying there are advantages overall to learning the color scheme and starting with all the centers first. Other people may actually find it easier and more enjoyable to do it that way.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Tue Sep 24, 2013 4:08 pm 
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Konrad wrote:
doctor twist wrote:

Instead of just doing R and "solve it again", I use a sequence of 8 turns that preserves the small edges.
The result is a 3-cycle that is pure regarding small edges.



Thank you Konrad, your algorithm is very easy to memorize and very effective. It works also to cycle three centers of the pyraminx. I guess that algorithm is quite useful for many puzzles.
Never the less I understood that it is more precise to avoid this parity case from the very beginning.


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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Wed Sep 25, 2013 10:41 am 
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I woke up this morning thinking about Konrad's statement:
Quote:
This would require much more memorizing of the colour scheme. As rline, I memorize a single face only.

Let's see how much really needs to be memorized to know the color scheme of the version 1 Gem V.

Let's say I grab the scrambled puzzle and orient it so that the white triangle is facing me in the top half of the puzzle and the blue triangle is in back in the top half of the puzzle. There is a square face between them.

So far, what have I had to memorize? White/Blue big triangles front and back.

Now I think about the small triangles. I did not have to memorize anything here because they are oriented opposite big triangles, and follow the color scheme of a standard Rubik's Cube. That is the small center below the white one is green when solved, since green is opposite blue. The small center to the right must be orange since it is opposite the large red center on the lower left. The small center to the left must be pink since it is opposite the purple one. Pink and purple are the two colors that are not on the Rubik's Cube, but that is not an issue, since they are paired in this puzzle as opposites. And the one in back is yellow, opposite the big white in front.

So I know where all the large centers and all the small centers go based on knowing the standard color scheme of the Rubik's Cube. So far, what have I had to memorize? White/Blue big triangles front and back.

Now the square faces. I memorize that between the white and blue hex faces there is a yellow square face. And to the lower right of the white hexagon face is a blue square face. If I know the color scheme of a standard Rubik's Cube, then all the rest falls into place. That's right, the square face colors are oriented exactly as a standard Rubik's Cube.

So far, what have I had to memorize? white / blue triangles front and back. yellow / blue strips up and right. Everything else falls into place from there.

So, it turns out it is not much memorizing at all. :P

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Fri Sep 27, 2013 9:18 am 
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Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
robertpauljr wrote:
....So, it turns out it is not much memorizing at all. :P
You are right, it is not much to memorize for a "parity avoidance" strategy. I have done it several times by now and it is pretty straight forward. :)
On the other hand, the 8 move sequence is well known to me from my Master Skewb method, so it was not much of a burden either. Anyway, I agree that it is easy enough to avoid this parity from the very beginning.

I'll see if the stripes on the full coloured version will influence me on using a different approach than currently.
(I'm still waiting for it and for a bunch of other puzzles from hknowstore.)

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Fri Sep 27, 2013 9:59 am 
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Location: Northern Central California
Konrad wrote:
robertpauljr wrote:
....So, it turns out it is not much memorizing at all. :P
You are right, it is not much to memorize for a "parity avoidance" strategy. I have done it several times by now and it is pretty straight forward. :)
On the other hand, the 8 move sequence is well known to me from my Master Skewb method, so it was not much of a burden either. Anyway, I agree that it is easy enough to avoid this parity from the very beginning.

I'll see if the stripes on the full coloured version will influence me on using a different approach than currently.
(I'm still waiting for it and for a bunch of other puzzles from hknowstore.)

Thanks for trying it out, and giving a positive report.

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 Post subject: Re: Solving the Dayan Gem V
PostPosted: Wed Oct 02, 2013 3:50 pm 
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Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Today, I have received the Gem V in coloured plastic.
I think, the strips do not add much difficulty.

I tried two alternatives
A. as described by robertpauljr on September 11th
B. as on my purple version before, just building triple composed edges (strip + two large edges), wherever the strips happen to be. Place these triples at the end via [1,1]

B requires less memorizing of the colour scheme. Therefore, I prefer it.
I like both variants better than doing the small edges (corners) last.

I'm not sure, if I really needed both variants (coloured plastic + single coloured body) :roll:
The purple body with stickers looks nicer, though.

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