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 Post subject: Arrow Planet by OSKAR
PostPosted: Sat Dec 04, 2010 8:14 am 
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Hi Twisty Puzzles fans,

Arrow Planet is a twisty puzzle with 52 arrowed squares moving around a sphere. But also the sphere parts can turn. This puzzle combines jumbling, fudging and sliding.

The geometry of the Arrow Planet is quite unusual. It has four axes at an angle of 81.2174 degrees, instead of the 90 degrees for a regular Rubik's Cube. As it result, this geometry jumbles.

The puzzle has four circles of slidey squares that turn around the four axes, each circle intersecting with other circles at a 90-degree angle. You can imagine my surprise when I discovered that this geometry has exactly THIRTEEN (13) squares in each circle. Well, not exactly 13, but 13.1086. I did a bit of fudging to make it fit, so that you would not know if I would not have told you.

As the four circles are not great circles of the sphere, there are little wedge-shaped voids between the squares. I filled these voids with little wedge-shaped pieces.

The 52 square pieces and the 70 wedge-shaped pieces are all stickered. The puzzle has six circles of one color when solved. The red, yellow, green and blue are continuous circles. The white and orange are interrupted circles.

This puzzle combines learning experiences from Distorted Cube, Mixup Cube and Number Planet. It runs very smoothly.

Watch the YouTube video.
Buy the puzzle from my Shapeways Shop.
Read more at the Shapeways Forum.
Check out the photos below.

Enjoy!

Oskar
Attachment:
Arrow Planet v2 - prototype - view 1.jpg
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Arrow Planet v2 - prototype - view 2.jpg
Arrow Planet v2 - prototype - view 2.jpg [ 53.09 KiB | Viewed 3715 times ]

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Arrow Planet v2 - prototype - view 3.jpg
Arrow Planet v2 - prototype - view 3.jpg [ 53.39 KiB | Viewed 3715 times ]

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Arrow Planet v2 - prototype - view 4.jpg
Arrow Planet v2 - prototype - view 4.jpg [ 54.74 KiB | Viewed 3715 times ]

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Arrow Planet v2 - prototype - view 5.jpg
Arrow Planet v2 - prototype - view 5.jpg [ 52.94 KiB | Viewed 3715 times ]

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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sat Dec 04, 2010 8:24 am 
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That is one of the craziest puzzles I've ever seen. But for some reason I really do love this puzzle. It looks like it would be a pain to solve.

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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sat Dec 04, 2010 8:28 am 
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This puzzle looks really confusing and, as SEBUVER said, a pain to solve. I like the idea of the puzzle, but I don't really like the look of the puzzle, with the light sphere, the dark tiles and then stripes all over it. :?

Alex

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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sat Dec 04, 2010 9:00 am 
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Could you give a more detailed explanation of how the axis work on this thing? I can't quite make out where the centers are to begin with. Are they near the vertices of a tetrahedron, but moved slightly?


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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sat Dec 04, 2010 9:37 am 
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WOW. I am VERY confused. Awesome job. :shock:

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PB: At home (In Competition)
2x2 1.xx (2.88)
3x3 11.xx (15.81)
4x4 1:18.26 (1:24.63)
5x5 (3:00.02)
6x6 4:26.05 (6:34.68)
7x7 6:38.74 (9:48.81)
OH (35.63)

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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sat Dec 04, 2010 10:14 am 
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APJ wrote:
This puzzle looks really confusing and, as SEBUVER said, a pain to solve. I like the idea of the puzzle, but I don't really like the look of the puzzle, with the light sphere, the dark tiles and then stripes all over it. :?

Alex


Second that!

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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sat Dec 04, 2010 12:01 pm 
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Bram wrote:
Could you give a more detailed explanation of how the axis work on this thing?
Hi Bram,

The attached 3D PDF should help you understand this geometry better. When you open the 3D-PDF, use your mouse to drag the sphere for different views.
Bram wrote:
Are they near the vertices of a tetrahedron, but moved slightly?
No. A tetrahedron has an angle of 109.471 degrees between its axes. A cube has an angle of 90 degrees. Arrow Planet has 81.2174. So it is closer to a cube.
APJ wrote:
I don't really like the look of the puzzle, with the light sphere, the dark tiles and then stripes all over it. :?
Stickering this puzzle poses quite a dilemma. There is no "classic" way to sticker this puzzle. Moreover, the squares have orientation, which should be reflected in the stickering. I am open to suggestions to improve the looks, although I won't implement them until after my first sale of this puzzle.

Oskar
Attachment:
Arrow Planet v2 - geometry - view 1.jpg
Arrow Planet v2 - geometry - view 1.jpg [ 73.27 KiB | Viewed 3592 times ]

Attachment:
Arrow Planet v2 - geometry.pdf [1.79 MiB]
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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sat Dec 04, 2010 12:12 pm 
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Joined: Sun Jun 13, 2010 1:00 am
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This is a great puzzle.

When I first learned about custom puzzles many of Tony's creations were amazing. I spent hours watching the 7x7x7 barrel wondering how it worked. As I started understanding puzzles, this magic faded. Then I saw the 24 cube and again was amazed. Now I design puzzles myself and can quickly figure out what I'm looking at. Puzzles are like magic tricks. Many lost their amazement as I became a magician myself and learned how to preform the tricks. With this puzzle Oskar, I am once again amazed. I have no clue how this trick works.
10/10 :mrgreen:

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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sat Dec 04, 2010 2:09 pm 
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This is great! I can't figure out if it is a twisty puzzle or a sliding puzzle...seems like the line between them here has been blurred.

Also some of the youtube comments are absolutely priceless! :lol:

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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sat Dec 04, 2010 4:24 pm 
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Garrett wrote:
This is great! I can't figure out if it is a twisty puzzle or a sliding puzzle...seems like the line between them here has been blurred.

Also some of the youtube comments are absolutely priceless! :lol:


I just laughed harder than I have in a very, very long time.

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~Kapusta

PB: At home (In Competition)
2x2 1.xx (2.88)
3x3 11.xx (15.81)
4x4 1:18.26 (1:24.63)
5x5 (3:00.02)
6x6 4:26.05 (6:34.68)
7x7 6:38.74 (9:48.81)
OH (35.63)

Current Goals:
7x7 sub 6:30
4x4 sub 1:10


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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sat Dec 04, 2010 10:48 pm 
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Location: Incheon, Korea
Wow, It is really awesome puzzle Oskar!
colorful, beautiful and very looks cool.
I really love it.
graet work!

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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sun Dec 05, 2010 12:21 am 
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It is of my opinion that this is the best twisty puzzle ever made. It is very aesthetically pleasing, it has a very challenging (and unique) solve, the design combines three advanced concepts (two of which no one else has even tried) and, it works well. I hope this puzzle get the recognition it deserves by being in the running for puzzle of the year.

Oskar, you are so far beyond everyone else in the puzzling world it's almost unfair.

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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sun Dec 05, 2010 9:46 am 
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That 3d pdf helps a lot. There's an aspect of the geometry I still don't understand though. It looks like the angle between the axis could be varied continuously and it would work at all values, what's keeping it at the very specific angle you've selected?


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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sun Dec 05, 2010 9:57 am 
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Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
Looking at this some more, I see this puzzle is sort of like a 6x6x6 which has been distorted a bit to allow for pieces to be added in a very odd way.

It's sort of a cousin of my suggestion for Distorted Cube II, which I think you should make because that one would be a lot of fun :-)


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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sun Dec 05, 2010 11:28 am 
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Bram wrote:
It looks like the angle between the axis could be varied continuously and it would work at all values, what's keeping it at the very specific angle you've selected?
Bram,

You are correct if it were only for the jumbling. The axes angle is 92 degrees for Distorted Cube, which jumbles similarly to Arrow Planet. But I could easily have chosen any other angle, like 85, 91 or 95 degrees. I just liked the looks of the results when choosing 92 degrees.

The options are more limited for Arrow Planet. I know that you like dimension analysis, so let's look at the problem from that perspective.
The Arrow Planet geometry has two degrees of freedom.
    1) The angle of the axis for the jumbling
    2) The radius of the circle for the slidey pieces
There are three restrictions, see also the Figure below.
    a) The circles should intersect at 90 degrees on the surface of the sphere. So for a given angle, the radius is determined, or vice verse.
    b) The ratio "a/b" between intersections of circles should be a rational number (e.g. 1/2)
    c) The ratio "a/c" between intersections of circles should also be a rational number

Obviously, this problem is over-specified. I have not been able to find any exact solutions, which may not exist at all. So what I did is starting with only restrictions a) and b), and then try some discrete numbers for the a/b ration, e.g. 1/1, 2/1, 1/2, 2/3, 3/1, 1/3, 1/4, 3/4, 3/5 etcetera. For each "candidate", I checked the a/c ratio. For a/b=1/2, I found a/c=1/2.1087, which is very close to 1/2. It is good that it is a bit larger than 1/2, as this is just the little bit of clearance that is needed to make the slidey pieces run smoothly.

So, can you now imagine my surprise when I discovered this unique geometry, based on the number thirteen?

Oskar
Attachment:
Arrow Planet v2 - geometry - view 3.jpg
Arrow Planet v2 - geometry - view 3.jpg [ 38.03 KiB | Viewed 3218 times ]

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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Sun Dec 05, 2010 2:59 pm 
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Location: Marin, CA
Ah, I understand now, it's all about the bands. Going for more pieces would undoubtedly get long thin bands which didn't add much to the puzzle, it's neat that this one (comes close to) lining up so nicely.

There are two ways you could have unbandaged the parts parts on the far side. You went for the mirror symmetric one instead of the rotationally symmetric one. I have no opinion as to which one is better, just found it interesting that there's the option.

I hope I'm not beating a dead horse, but you should really revisit the Distorted Cube again. The last one you did seemed to have a complex geometry with too many angles where it was unclear whether things were supposed to line up or not, and at least one way a piece could just plain fall out, and I think my suggestion for how to do the geometry such that there are only two different edge angles in the whole thing would work nicely.


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 Post subject: Re: Arrow Planet by OSKAR
PostPosted: Tue Dec 07, 2010 2:32 pm 
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Bram wrote:
There are two ways you could have unbandaged the parts parts on the far side. You went for the mirror symmetric one instead of the rotationally symmetric one. I have no opinion as to which one is better, just found it interesting that there's the option.
Bram,

Well spotted. The two options are just stickers mods of each other.

Oskar

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