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 Post subject: PentaJumble by OSKAR
PostPosted: Sat Jul 30, 2011 1:37 pm 
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Hi Twisty Puzzles fans,

PentaJumble is based on a geometry that was suggested by Bram Cohen. The puzzle has four pentagonal faces that can be rotated. The puzzle jumbles, which causes some strange bandaging. The puzzle has all kinds of weird geometric properties, some of which even Bram may not have anticipated. For starters, all edges can be interchanged. Moreover, there are many different ways to assemble the puzzle, such that it has the same outer shape, but different different positions of the little wedge-triangles.

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

Enjoy!

Oskar
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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sat Jul 30, 2011 1:48 pm 
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The only way I could understand this puzzle would be to hold it in my hands. And if I ever scrambled it, that's the way it remain! Nice puzzle Oskar.

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sat Jul 30, 2011 1:50 pm 
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awesome! I love the shape of the puzzle

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sat Jul 30, 2011 2:15 pm 
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Wow. That puzzle is really weird. I like it though! Well done Oskar. :)

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sat Jul 30, 2011 3:18 pm 
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Once again, I am in complete awe of your puzzle. Also, can you show us a picture of the differently assembled puzzle or at least describe how it would change the solving experience of it?

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sat Jul 30, 2011 4:18 pm 
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damn hard puzzle ,i even don't know wich are the notation,because if i'll say R the answer will be wich R? :lol:

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sat Jul 30, 2011 5:02 pm 
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Sometimes I wonder if you're actually human... Like now. :scrambled:

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sat Jul 30, 2011 5:34 pm 
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thomasbomb wrote:
Sometimes I wonder if you're actually human... Like now.
(what she said)

Nice puzzle Oskar, I like all those jumbling and fudged puzzles, but I find them quite complicated :lol:

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sat Jul 30, 2011 9:02 pm 
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I have literally run out of things to say about your crazy-complicated puzzles oskar. And I don't really want to be yet another person who says "Wow! Fantastic puzzle as always!" but its the truth!

I am particularly interested in the fact that in can be assembled in multiple ways- all (or many?) of which are independent and subtly different puzzles in their own right. Is there some complex mathematical formula that you can use to work out just how many puzzles you can make with this one "kit"? Maybe you should offer complementary 3d PDF files of the innards to whomever buys one! That should aid the assembly process.

And sorry for the off topic, but Oskar, are there any new developments in what we discussed a few months ago? PM me if you want :)

Will


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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sat Jul 30, 2011 11:50 pm 
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So Oskar really does release one puzzle per week? I thought that was exaggeration...

[genericcomment]Awesome job, again![/genericcomment]

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sun Jul 31, 2011 1:30 am 
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I even needed some minutes to figure out the symmetry group of this puzzle.
Very strange puzzle.


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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sun Jul 31, 2011 5:24 am 
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Andreas Nortmann wrote:
I even needed some minutes to figure out the symmetry group of this puzzle.
I'm surpirised that you actually managed to find one. :shock:

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sun Jul 31, 2011 7:58 am 
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awsome as always. Is incredible your work capacity

keep working, is fantastic to see your puzzles!!

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sun Jul 31, 2011 12:49 pm 
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Wow!!! Many many questions...
Oskar wrote:
Moreover, there are many different ways to assemble the puzzle, such that it has the same outer shape, but different different positions of the little wedge-triangles.
(1) How many?
(2) Are they all independent?
(3) Can you get from one to some or all of the others without taking the puzzle apart?
(4) If yes, how many closed groups are there?
(5) If 2 or more are some of them mirror copies of each other... and thus the same puzzle solving experience?
(6) Could you post a video showing a few of the options that come up during assembly?
DudeHuLubeDaRubeCube wrote:
I am particularly interested in the fact that in can be assembled in multiple ways- all (or many?) of which are independent and subtly different puzzles in their own right. Is there some complex mathematical formula that you can use to work out just how many puzzles you can make with this one "kit"?
Basically what he said... I'm wanting to understand this property and I'm clueless at the moment.
Andreas Nortmann wrote:
I even needed some minutes to figure out the symmetry group of this puzzle.
Very strange puzzle.
So... what is it? My brain is already fried.

Carl

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Sun Jul 31, 2011 1:05 pm 
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Nice job! Like you said, it scrambles like hell. :D Anyway, amazing job. Solving that would be quite a feat.


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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Mon Aug 01, 2011 11:44 am 
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Nice Job Oskar! I think if I jumbled that, it would never be the same.

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Mon Aug 01, 2011 12:49 pm 
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wwwmwww wrote:
Andreas Nortmann wrote:
I even needed some minutes to figure out the symmetry group of this puzzle.
Very strange puzzle.
So... what is it? My brain is already fried.
To be precise it is a subgroup of Oh which is the symmetry group of the hexahedron, octahedron and others.
This subgroup is isomorph to D2d:
You might look here:
http://en.wikipedia.org/wiki/Octahedral_symmetry

It has 8 members:
  • Identity
  • 1 × rotation by 180° about a 4-fold axis
  • 2 × rotation by 180° about a 2-fold axis
  • 2 × reflection in a plane perpendicular to a 4-fold axis
  • 2 × rotoreflection by 90°
Please note that I have taken these names from the wikipedia article.
Andreas


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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Mon Aug 01, 2011 3:46 pm 
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If I am not mistaken, this shape is the combinatorial dual of the snub disphenoid (http://en.wikipedia.org/wiki/Snub_disphenoid).
Edit: Referring to the vertex graphs, this is correct, although taking the centroids of the faces of this puzzle as the vertices of the dual does not quite make equilateral triangles.
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Picture 5.png
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Picture 7.png
Picture 7.png [ 47.12 KiB | Viewed 3423 times ]

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Last edited by contrabass on Thu Aug 04, 2011 12:14 pm, edited 2 times in total.

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Tue Aug 02, 2011 8:05 am 
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contrabass wrote:
If I am not mistaken, this shape is the combinatorial dual of the snub disphenoid (http://en.wikipedia.org/wiki/Snub_disphenoid).
You may be wrong ...

EDIT: I drew the dual of my shape by drawing lines from the surfaces orthogonally to the origin. The resulting shape is very similar to a snub disphenoid indeed. However, unlike the snub disphenoid, the triangles are NOT equilateral. But close ...

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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Mon Aug 08, 2011 12:37 am 
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An interesting property of this puzzle is that even though all the turns are rational angles, it still appears to be impossible to unbandage it to a doctrinaire puzzle (that is, it actually jumbles). I used to think that in general if something looks like it jumbles, then it does, but it turns out that Battle Gears, which I thought jumbled, is in fact just bandaged, leading to this puzzle being the leading contender for a rational-angles-only jumbling puzzle. Does anybody have a better than wild guess on whether this puzzle jumbles? That is, a proof that it jumbles, or a complete unbandaging?


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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Mon Aug 08, 2011 1:15 am 
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Bram, even though the turns are at rational angles, I don't think the angles between the faces are... but I could be wrong. Does that matter?

Oskar, could you make a picture of what this would look like as a sphere?


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 Post subject: Re: PentaJumble by OSKAR
PostPosted: Mon Aug 08, 2011 3:03 am 
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I've finally figured out this thing after studying the pictures: The puzzles consists of four regular pentagons joined together in a ring-like fasion, with four congruent trapezoids closing off the remaining sides. Each trapezoid borders three pentagons and one other trapezoid; each pentagon borders two other pentagons and three trapezoids.The trapezoids have three edges of equal length bordering the pentagons, with the remaining edge being shorter than the other three. There are two short edges on the puzzle, each connecting a pair of trapezoids, twelve long edges connecting the trapezoids to the pentagons, and four long edges joining pentagon to pentagon. Lastly, there are four corners connecting two trapezoids to one pentagon, and eight corners connecting two pentagons to one trapezoid.

All together, that makes:
4 pentagons + 4 trapezoids = 8 faces
2 short trap/trap edges + 8 long pent/trap edges + 4 long pent/pent edges = 18 edges
4 trap/trap/pent vertices + 8 trap/pent/pent vertices = 12 vertices

8 faces + 12 vertices = 18 edges - 2
The laws of polyhedral geometry hold.

By the way, does this solid have a name? :scrambled:
Jared wrote:
Bram, even though the turns are at rational angles, I don't think the angles between the faces are... but I could be wrong. Does that matter?

The cube is the only Platonic solid with a rational angle between adjacent faces; it is tilable in 3d space, proving because the square angles are rational. Tetrahedrons and octahedrons can also tile 3D space by filing into an alternating grid; the angles of each are irrational, but they add up to 180 degrees. Cubes, tetrahedrons, octahedrons, and dodecahedrons do not jumble; only the icosahedron does.

As a counterexample, the rhombic dodecahedron tiles 3d-space very well; the angle between two faces is 120 degrees; it is the optimal solution to the sphere-packing question. Despite the faces meeting at rational angles, the faces themselves are rhombi with irrational vertice angles, and yes, the rhombic dodecahedron also jumbles.

So, I think it is fair to say, that whether or not faces meet at rational angles is not a good determining factor of whether the face-turning version of that geometry jumbles or not.

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