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 Post subject: Rob's Pyraminx by OSKAR
PostPosted: Sat Mar 22, 2014 4:26 am 
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Hi Twisty Puzzles fans,

Rob's Pyraminx was suggested at Rob Stegmann's puzzle website. When analyzing all twisty puzzles with a tetrahedral geometry, Rob found an edge-less pyraminx design that has not yet been implemented. Here it is. It has a Skewb mechanism inside, so the puzzle is a shape mod of the Skewb.

This puzzle is arguably the easiest non-trivial twisty puzzle :-). What is it's God's number?

Watch the YouTube video.
Buy the puzzle at my Shapeways Shop.
Read more at the Shapeways Forum.
Try the simulator by Aditya Sriram.
Check out the photos below.

Enjoy!

Oskar
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Last edited by Oskar on Sat Apr 05, 2014 7:51 am, edited 1 time in total.

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sat Mar 22, 2014 5:40 am 
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Awesome puzzle! Given that the Pyraminx and the Skewb both have God's numbers of 11 (if I recall correctly), I would assume that the God's number for this puzzle would be 11 or lower. That's the best that I can do, considering that I'm really not all that educated in mathematics. I am very good at drooling over new puzzles though. 8-)

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sat Mar 22, 2014 8:12 am 
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prettily puzzle!

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sat Mar 22, 2014 10:01 am 
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I love this puzzle. Be it easy or not, it's lovely :)

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sat Mar 22, 2014 4:32 pm 
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I like it, too! :D
Another slot filled.
Thanks, Oskar.

My twisty family tree chart of octahedrons missed the analogue of this, but of course it is possible, too.

I haven't tried to figure God's Number for this but I am sure Jaap can figure it out... :-)

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sat Mar 22, 2014 4:52 pm 
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I'm sure the number is four because that is how many axes there are. One could simply orient the first two corners without placing any centers, but this depends on which two corners and in what order because of the next two turns. Then, the third corner orientation would bring in the shared center of the three oriented corners, as well as place the other two affected centers in their relative spots on the final corner. Then, the final corner would bring all of the centers into their correct spots, as well as orient itself. That is my theory. No math is involved, so it may or may not be correct.

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sat Mar 22, 2014 5:10 pm 
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I say 8 is god's number for this puzzle.

My explanation is that 7 is too few, 9 is too many, and based on how many visible part can be postitioned, I say 8 (4 "centers" and 4 stationary parts)

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sat Mar 22, 2014 8:43 pm 
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I'm gonna guess 8. Each vertex can be correctly oriented in one move each. The centers should at most need a 2-2 swap, which can be done with a [1:1] commutator. 4+4 = 8.

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sun Mar 23, 2014 1:54 am 
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If I adapt Jaaps explanation of the Skewb this puzzle has 324 permutations.
In the worst case you need four moves to correct the orientations of the corners.
Everything else you have to do is placing one center while correcting the corners.
Therefore I second BelcherBoy2000 and vote for four.

A very neat slot-filler.
A corners-only skewb.


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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sun Mar 23, 2014 4:34 am 
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Rob wrote:
My twisty family tree chart of octahedrons missed the analogue of this.
That would be a corner-turning no-edges octahedron using a regular 3x3x3 cube mechanism, correct? And how about a corner-turning no-edges icosahedron with a regular megaminx mechanism?
Andreas Nortmann wrote:
Therefore I second BelcherBoy2000 and vote for four.
Hey, a God's number is not decided by popular vote! Perhaps on YouTube, but not at the Twisty Puzzles Forum?

Oskar

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sun Mar 23, 2014 9:05 am 
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I agree that the god's number is 4. However, I can think of an easier non-trivial puzzle. A 2x2x2 that has 4 white cubies, and 4 black cubies, where the solved state is a checkerboard on each side, would have a god's number of 3.

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sat Apr 05, 2014 7:52 am 
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Simulator of Rob's Pyraminx by Aditya Sriram.

Oskar

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sun May 25, 2014 10:11 am 
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I made some special stickers for Rob's Pyraminx, because I felt, that
the stickers have so strong geometric shapes. Hope you like it.


Attachments:
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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sun May 25, 2014 10:47 am 
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Frank,

That looks great!

Why didn't you pattern the center face? Faces with orientation would make the puzzle (even) harder.

Oskar

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sun May 25, 2014 11:10 am 
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I thought about that, but finally came to the decision that more decoration would perhaps be an overkill.
But the orientation of the centers would indeed give the puzzle a higher degree of complexity.
May be I can find a nice design for that, too.

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Thu May 29, 2014 5:59 am 
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Oskar wrote:
Rob wrote:
My twisty family tree chart of octahedrons missed the analogue of this.
That would be a corner-turning no-edges octahedron using a regular 3x3x3 cube mechanism, correct? And how about a corner-turning no-edges icosahedron with a regular megaminx mechanism?
Andreas Nortmann wrote:
Therefore I second BelcherBoy2000 and vote for four.
Hey, a God's number is not decided by popular vote! Perhaps on YouTube, but not at the Twisty Puzzles Forum?

Oskar


Four should be correct. You need at least four moves, because it might be necessary to turn all four tips.
If you do it in the right sequence you can arrange the centers in a way that they are correct in place after these four moves.
So you won't need more than four.

If the centers get an orientation by additional decoration as suggested, the center orientation will need additional moves.
If this is 11, as mentioned for a common Skewb, I'm not sure about.

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Tue Jun 10, 2014 2:46 pm 
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I had the opportunity to play with this puzzle for a good while last weekend, and came to the conclusion that God's algorithm is indeed 4. It is not totally obvious though, so when I got home I ran it through my computer program to be sure:
depth 0, positions 1, total 1
depth 1, positions 8, total 9
depth 2, positions 48, total 57
depth 3, positions 188, total 245
depth 4, positions 79, total 324

If none of the tips are correctly oriented, then the moves you need to do to fix the tips can be reordered in such a way that the centres fall into place. You only need to worry about one centre, as the other three will then automatically be solved. If some tips are already correctly oriented, then you may need to twist some tip twice to to give you sufficient moves to provide enough reordering options for solving the centres.

If the orientations of the centres is visible, then this becomes 7 moves:
depth 0, positions 1, total 1
depth 1, positions 8, total 9
depth 2, positions 48, total 57
depth 3, positions 280, total 337
depth 4, positions 1403, total 1740
depth 5, positions 4132, total 5872
depth 6, positions 2771, total 8643
depth 7, positions 105, total 8748
[EDIT: These numbers are incorrect. See below for corrected version.]
I hope these numbers are correct as I may well have made a mistake in defining the puzzle in my program.

Note that in this case there are not 3^4 but 3^3 times as many positions because there is a simple twist constraint. Each tip twist move can be considered equivalent to a face turn of the opposite face. In the latter point of view you hold the core and its face centres fixed in space. So a move not only twists one tip (relative to the vertices), it also twists one centre (relative to the core), so the total tip twist must equal the total centres twist.

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Last edited by jaap on Wed Jun 25, 2014 5:16 am, edited 1 time in total.

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Tue Jun 10, 2014 11:45 pm 
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Thank you Jaap,
I will edit the entry for Rob's Pyraminx.

Andreas


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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Fri Jun 13, 2014 3:31 pm 
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(below post is written by Oscar Roth Andersen)
Proof-by-hand of God's number:
Okay, so first we realise that for any 0 mod 3 orientation of corners, a solved center results in a correct permutation of the rest of the centers*. In other words, if we solve a layer (leaving 1 corner + 3 centers) we can always solve the rest in a maximum 1 move.

Below is a table showing solutions to solve 3 corners + 1 center for all unique cases. (I didn't sort out symmetry or inverses, only rotations.)
Image
(1=1 clockwise turn in order to solve corner, 2=2 clockwise (or 1 counterclockwise))

As seen in above table it is always possible to solve 3 corners + 1 center in 3 turns for the worst case, hence making that upper bound 3+1=4 moves.
The lower bound is trivially 4 because of the 4 non-permutable corners, hence making God's number 4.

---------------
Jaap, your numbers are incorrect.
Your table indicates that for the solved case there exists a non-trivial solution of 5-6 moves. I can't find any, instead I found this:
Depth 1
Depth 2
Depth 3
Depth 4
Depth 5
Depth 6
Depth 7
Depth 8
R L R L' R' D' L' D
R L R U R' U' R' L'
...
D' U' D' R D L D R'
D' U' D' L' D R D L

So that indicates depth 1: 8=8, dept 2: 8*6=48, depth 3: 8*6*6=288. But to verify this I did a full God's Algorithm table on the puzzle and got this:

Moves Positions
0 1
1 8
2 48
3 288
4 1436
5 4286
6 2636
7 45
Total positions: 8748

---------------
* = It is a very easy to see this nature on the skewb (therefore I omitted it), but if anyone would like a real proof of it to understand why it holds I would be glad to write it, but it's a bit long (and I guess someone else here can explain it in fewer words than me).

/Odder


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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Wed Jun 18, 2014 12:42 am 
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So I see this is getting mass produced by Mefferts :)

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Wed Jun 18, 2014 6:32 am 
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nice

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Wed Jun 18, 2014 7:21 am 
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Wow! Great news!
I hope this means Rob's Octahedron is also coming!! :D

martywolfman wrote:
So I see this is getting mass produced by Mefferts :)


juanan wrote:
nice


Where are you finding this info???


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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Wed Jun 18, 2014 7:24 pm 
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Part of me is like "Cool!" and another part of me is like "Why?"


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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Fri Jun 20, 2014 12:40 pm 
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Jared wrote:
Part of me is like "Cool!" and another part of me is like "Why?"

It's a new puzzle, that's why. Easy cheap ones are very popular.

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sat Jun 21, 2014 12:48 pm 
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It's now available for sale from Mefferts and the Jade Club

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sat Jun 21, 2014 1:07 pm 
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Great,
One for my collection.

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sat Jun 21, 2014 5:25 pm 
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I've ordered mine ! 2 minutes after that the Tony Fisher's video was online :mrgreen:

I've take the black version, I think I'm the first french person to ordering this puzzle


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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sat Jun 21, 2014 8:25 pm 
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Photos.


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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sun Jun 22, 2014 4:22 am 
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Tony, I saw that your video came online at exactly the same time as RedKB's and crazybadcuber's. Is this a request from Mefferts?

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sun Jun 22, 2014 4:34 am 
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1NSAN3 wrote:
Tony, I saw that your video came online at exactly the same time as RedKB's and crazybadcuber's. Is this a request from Mefferts?
All coordinated:
YouTube video:
https://www.youtube.com/watch?v=7dUJOHdaP9g
https://www.youtube.com/watch?v=HeRDHZq31Cg
https://www.youtube.com/watch?v=lG7ELzxrL4A
https://www.youtube.com/watch?v=71BML4J-D-8
https://www.youtube.com/watch?v=fjYswpuXQ08
Product pages:
http://www.mefferts.com/products/detail ... 13&id=1035
http://www.mefferts.com/products/detail ... 13&id=1036
http://www.mefferts.com/products/detail ... 13&id=1037

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sun Jun 22, 2014 5:35 am 
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Nice puzzle! Another pyraminx variation in my collection.

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Wed Jun 25, 2014 5:14 am 
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guinepigsrock wrote:
(below post is written by Oscar Roth Andersen)
<snip>
Jaap, your numbers are incorrect.
<snip>
Moves Positions
0 1
1 8
2 48
3 288
4 1436
5 4286
6 2636
7 45
Total positions: 8748


You are correct. I have now confirmed these numbers. I had made a mistake in specifying the centre orientation changes that the moves make.

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Wed Jun 25, 2014 1:42 pm 
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What would this look like as a cube?


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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Wed Jun 25, 2014 2:41 pm 
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Jared wrote:
What would this look like as a cube?

Square, consisting of 6 sides. :lol:

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Wed Jun 25, 2014 9:38 pm 
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1NSAN3 wrote:
Jared wrote:
What would this look like as a cube?

Square, consisting of 6 sides. :lol:

Cubical, consisting of 6 square sides.

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 Post subject: Re: Rob's Pyraminx by OSKAR
PostPosted: Sat Jul 05, 2014 5:37 am 
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I just discovered that the concept of "Rob's Pyraminx" was posted by Daqing Bao (a.k.a. Dayan) here on 20 December 2009. It is the sketch at the bottom center.
Image
I checked this with Rob. His chart is from 7 June 2009. It was referenced in a post of 11 December 2009 as "a while ago". The "wayback-machine" has a snapshot of the chart dated 12 December. Apparently, Rob was first by several months.
Image
Again an interesting case of near-parallel invention. Even more interesting is the question why such a nice concept went unnoticed for more nearly five years.

Oskar

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