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 Post subject: Deep Penta by OSKAR
PostPosted: Sat Jun 15, 2013 5:28 am 
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Hi Twisty Puzzles fans,

Deep Penta is a design inspired by the "deeper-than-origin" discussion at the Twisty Puzzles Forum, triggered by David Pitcher's RotoPrism 2.

The purpose of the big hole in one of the corners is to show that the mechanism of the puzzle is deeper-than-origin. However, only two deeper-than-origin rotations are enabled (two screws at the inside). Some shallow-cut rotations are enabled too (screws visible at the outside), but not all. This makes the puzzle confusing to solve, as sometimes rotations are blocked. The screws are kept visible to reduce that confusion again.

There is something paradoxical about "deeper-than-origin". This puzzle is deeper-than-origin, because only some of the cuts are deeper-than-origin. If all cuts were deeper-than-origin, then the puzzle itself would no longer be classified as deeper-than-origin. Strange, isn't it?

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: Deep Penta by OSKAR
PostPosted: Sat Jun 15, 2013 6:03 am 
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Is this the "female" version of the Eight Inch Bolt? Or am I just seeing things I shouldn't?

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 Post subject: Re: Deep Penta by OSKAR
PostPosted: Sat Jun 15, 2013 6:22 am 
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KelvinS wrote:
Is this the "female" version of the Eight Inch Bolt? Or am I just seeing things I shouldn't?


Oh Kevin :roll:

On a slightly more serious note, why did you make the inside look like cheese?

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 Post subject: Re: Deep Penta by OSKAR
PostPosted: Sat Jun 15, 2013 7:51 am 
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Fantastic! This seems to me like a whole new classification of puzzle in which some axes are linked to other axes in such a way that they are relocated by movements of the first axes.

Is the puzzle difficult to solve?

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 Post subject: Re: Deep Penta by OSKAR
PostPosted: Sat Jun 15, 2013 10:12 am 
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rubikcollector123 wrote:
On a slightly more serious note, why did you make the inside look like cheese?
I made the core yellow, so people can see the inside well. The dye process was experimental. After I dyed the core yellow, I wrapped it in plastic, except the outer parts, and I dyed those black. However, bit of the black dye leaked through to the parts that should be yellow. Next time, I may use a black felt-tip pen.
David Pitcher wrote:
Is the puzzle difficult to solve?
It is quite easy. Just the deeper-than-origin-induced bandaging can be a bit confusing. Consider this puzzle a proof of concept.

Oskar

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 Post subject: Re: Deep Penta by OSKAR
PostPosted: Sat Jun 15, 2013 12:52 pm 
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I don't understand. How does this act functionally different from a regular pentagonal prism? Like, not why it's different, but what, mechanically, is going on to cause the differences?

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 Post subject: Re: Deep Penta by OSKAR
PostPosted: Sat Jun 15, 2013 2:16 pm 
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Ender Delphiki wrote:
How does this act functionally different from a regular pentagonal prism?
Some moves are blocked (like "internally bandaged").
Ender Delphiki wrote:
... what, mechanically, is going on to cause the differences?
The basis of this puzzle is a two-axes deeper-than-origin-cut Pentagonal Prism puzzle. That part works like, well, a deeper-than-origin-cut Pentagonal Prism puzzle, i.e. the core remains aligned with the smaller part when making a turn. The outer shell is a three-axes shallow-cut Pentagonal Prism. At start, all five axes point in a different direction, and all moves are enabled. However, after making some deeper-than-origin moves some of the outer axes are repositioned, resulting in turns that become blocked (bandaged) for lack of a rotation axes.

I hope that somebody else with better explanation skills can make it more clear.

Oskar

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 Post subject: Re: Deep Penta by OSKAR
PostPosted: Sat Jun 15, 2013 4:15 pm 
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Could you make the completely deep cut version of this with the holes in all the corners so you could see the shallow puzzle inside like you can see the megaminx inside the master pentultimate of TomZ's Multidodecahedron?

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 Post subject: Re: Deep Penta by OSKAR
PostPosted: Sun Jun 16, 2013 2:29 am 
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GuiltyBystander wrote:
Could you make the completely deep cut version of this with the holes in all the corners so you could see the shallow puzzle inside like you can see the megaminx inside the master pentultimate of TomZ's Multidodecahedron?
No.

The picture below shows the cut curves. The black cut curve is a three-shell deeper-than-origin with some extra zig-zags near the surface. The basis of the puzzle is using only two of those deeper-than-origin cuts, see the next picture. As you can see, one corner is not covered by cut curves. That is where is the hole. If one would make a completely deep-cut version with five deeper-than-origin cuts, then there is no room for a hole.

Oskar
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 Post subject: Re: Deep Penta by OSKAR
PostPosted: Mon Jun 17, 2013 10:00 pm 
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David Pitcher wrote:
Fantastic! This seems to me like a whole new classification of puzzle in which some axes are linked to other axes in such a way that they are relocated by movements of the first axes.


I commented on that phenomenon when trying to classify all the 3x3x3 cuboids. There's all kinds of crazy variations based on whether a particular motion is a slice motion or a two opposite faces motion, when the other four faces aren't all symmetric. Trying to list them all appears hopeless, even if you restrict it to cases where opposite faces must behave the same way. That said, I don't think anyone has ever actually built two 3x3x3 cuboids whose behavior only different in that one of them had a slice axis where the other one had a two opposite faces axis. It would be an interesting challenge for someone to design and build one.


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 Post subject: Re: Deep Penta by OSKAR
PostPosted: Tue Jun 18, 2013 1:22 pm 
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Bram wrote:
That said, I don't think anyone has ever actually built two 3x3x3 cuboids whose behavior only different in that one of them had a slice axis where the other one had a two opposite faces axis. It would be an interesting challenge for someone to design and build one.
Bram,

I do not understand the challenge. If I take HandiCube, and then I bandage the inner 2x2x2 into a 1x2x2 or a 1x1x2. The result would be two 3x3x3 cubes, one with one slice-only axis, and the other with two slice-only axes. Easy. What am I missing?

Oskar

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 Post subject: Re: Deep Penta by OSKAR
PostPosted: Thu Jun 20, 2013 11:29 am 
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Oskar wrote:
I do not understand the challenge. If I take HandiCube, and then I bandage the inner 2x2x2 into a 1x2x2 or a 1x1x2. The result would be two 3x3x3 cubes, one with one slice-only axis, and the other with two slice-only axes. Easy. What am I missing?


In that example the axes of the two cuboids behave very differently. In one there are two axes where opposite faces can turn, in the other there is only one. My challenge is to make two cuboids which have axes A, B, and X, where in one of them X is a slice only move and in the other it's an opposite faces turning move, where the difference is that in the second cuboid after you rotate 90 degrees the behaviors of the A and B axes will be swapped.


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