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 Post subject: Pegasus, a puzzle based on the 5D symmetry of the 5-simplex!
PostPosted: Wed Jul 28, 2010 11:46 am 
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So to continue with the "PAJUPUMA", here is a puzzle based on a higher dimension than the fourth...!


Attachment:
5D_Pegasus.jpg
5D_Pegasus.jpg [ 48.33 KiB | Viewed 1679 times ]


Unlike Chronos, Pegasus uses an even higher symmetry, which this time is derived from the 5th(!) dimension.
This equips the puzzle with more complex moves. More specifically, by using the "minimised external edges"
shape (MEES), we have now three choices for a movement, compared to only one found in Chronos. Each of those
choices provides a different result.

By using those three moves (and by studying their outcomes), as much amazing as it sounds, we may create
any color combination for the MEES.

Of course, the higher the dimensional symmetry, the more options and shapes we have to choose from.
What is shown in this video is just the tip of the iceberg of what can be done with this structure! (in general,
we can produce any of the 3D projections of the 5D structure known as 5-simplex)

Video here:

http://www.youtube.com/watch?v=H5M0Rlnj0EY

:)


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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 11:58 am 
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That one is maybe my favorite, with the Kronos because of it's simplicity

Less than 3!!

:D Greg :D

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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 12:02 pm 
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That looks very interesting. I don't really get the dimension idea in general, but they look so fun to play with!

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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 12:06 pm 
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SEBUVER wrote:
but they look so fun to play with!

Pantazis is the master of making puzzle TOYS. Even my girlfriend's friend plays with my cubedron. They're truly FUN, not just puzzles.

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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 12:09 pm 
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RubixFreakGreg wrote:
That one is maybe my favorite, with the Kronos because of it's simplicity

Less than 3!!

:D Greg :D


Yeap, I also like Pegasus a lot! :)

By the way, it is Chronos (one of the ancient Gods after the Universe was made),
and not Kronos (one of the Titans).

;)


SEBUVER wrote:
That looks very interesting. I don't really get the dimension idea in general, but they look so fun to play with!


The best part of those designs, is that by showing the different movements required,
anyone can enjoy playing with amazing symmetry properties (literally out of this 3D world!)
without the need to understand anything of higher dimensional background.

Isn't that wonderful?

:)


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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 12:20 pm 
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theVDude wrote:
SEBUVER wrote:
but they look so fun to play with!

Pantazis is the master of making puzzle TOYS. Even my girlfriend's friend plays with my cubedron. They're truly FUN, not just puzzles.


Thanks, it is what I am trying so hard to do! :)
(e.g. the DoTS, which is an "easy Cubedron").

The person playing with any of the puzzles/toys could be using
a structure based on some heavy mathematical theory.

But the main aim is to allow this person to have fun. And the best way
to do this, is to provide an attractive structure with "colorful ways".

Then, playing with the puzzle/toy becomes equivalent to learning
maths without knowing it!

I know this is evil, but in paradoxically angelic way!

:lol: :P


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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 12:24 pm 
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How about a gravity puzzle with 4-d symmetry?

More seriously, how are you deciding on all of these names?

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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 12:28 pm 
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The only thing I don't like about the current state of these puzzles is the fact the colors don't get mixed up :lol:

With this puzzle I really noticed it. Do you have any ideas on ways to color them so that the average person can know if it's solved or scrambled?

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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 12:34 pm 
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Rentlix wrote:
How about a gravity puzzle with 4-d symmetry?


LOL we do *not* want to mess up gravity *with* higher dimensions...
you don't know what weird objects could come out of that!!!
(hint: black hole warping, sucking us in and turning us inside-out! :lol: )


Rentlix wrote:
More seriously, how are you deciding on all of these names?


The names can be based on the names of the structures
(e.g. Hyperion - a powerful Titan - for the Hypercube),
or from the shape (e.g. the MEES of the 5-simplex somehow
reminds me of Pegasus LOL).

But I love to pick up names from the Greek mythology,
some of them sound very intimidating!

:)


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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 12:38 pm 
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kastellorizo wrote:
But I love to pick up names from the Greek mythology, some of them sound very intimidating!
Indeed, but I think Pegasus sounds more cute than scary :lol:

Very interesting puzzle, I have to say. But I don't fully understand the purpose of it. To alter the shape according to the level of dimensions, or can it actually be in a solved or an unsolved state?


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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 12:39 pm 
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PuzzleMaster6262 wrote:
The only thing I don't like about the current state of these puzzles is the fact the colors don't get mixed up :lol:

With this puzzle I really noticed it. Do you have any ideas on ways to color them so that the average person can know if it's solved or scrambled?


So far I am trying to pick up the simplest coloring themes for either corners or edges. :D
For example in Hyperion (Hypercube), someone could clearly see what is happening,
i.e. the blue cube containing the red cube and vice versa after going to a different solved state.

And I know exactly what you mean. I had a very hard time explaining how Chronos worked
at the IPP. I guess a two color theme would have helped more to explain.
(But then, it would have been less colorful!!! LOL)

:D


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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 12:44 pm 
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Katten wrote:
kastellorizo wrote:
But I love to pick up names from the Greek mythology, some of them sound very intimidating!
Indeed, but I think Pegasus sounds more cute than scary :lol:

Very interesting puzzle, I have to say. But I don't fully understand the purpose of it. To alter the shape according to the level of dimensions, or can it actually be in a solved or an unsolved state?


Pegasus was a very strong flying horse. I guess he "can* be cute, but is also very powerful. LOL :)

The goal is to:

1. always use the same shape (MEES = minimum external edges shape, i.e. all external
edges should be of minimum length, which provides a unique "Pegasus" like shape).
2. By using the three different available moves, the colors of the corners are exchanged.
So at this early stage, the goal is to play around and to enjoy the way the corners can
change colors while trying to achieve every possible combination (and that is not easy!)

:D


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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 1:03 pm 
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kastellorizo wrote:
Pegasus was a very strong flying horse. I guess he "can* be cute, but is also very powerful. LOL
That reminded me of the fact that I'm terrified of horses, which leads me to conclude that Pegasus is an intimidating name after all :lol:
kastellorizo wrote:
The goal is to:

1. always use the same shape (MEES = minimum external edges shape, i.e. all external edges should be of minimum length, which provides a unique "Pegasus" like shape).
2. By using the three different available moves, the colors of the corners are exchanged. So at this early stage, the goal is to play around and to enjoy the way the corners can change colors while trying to achieve every possible combination (and that is not easy!)
I see. Now that does sound like a challenge. So instead of having one defined solution, like the typical all-colors-on-its-correct-face-solution seen on a lot of puzzles, the goal is to achieve all possible permutations. How clever! I love the idea and the way the goal of this puzzle stands out from, say, a Rubik's Cube.


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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 5:06 pm 
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O thats were my radio antenna went :lol:
This is a really cool puzzle nice work


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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 5:10 pm 
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Was Chronos named because it is fourth dimensional, a concept which is often attached with time?

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 Post subject: Re: Pegasus, a puzzle based on the 5D symmetry of the 5-simp
PostPosted: Wed Jul 28, 2010 9:27 pm 
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Katten wrote:
I see. Now that does sound like a challenge. So instead of having one defined solution, like the typical all-colors-on-its-correct-face-solution seen on a lot of puzzles, the goal is to achieve all possible permutations. How clever! I love the idea and the way the goal of this puzzle stands out from, say, a Rubik's Cube.


I admit though, that this can be confusing to some people. But there *are* more ideas
to come, which when seen combined, then this type of movement will be more succinct. :)


eye2eye wrote:
O thats were my radio antenna went :lol:
This is a really cool puzzle nice work


LOL I ran out of car antennas, so now I am going for the radio ones.
Walkie-talkies are next!!! :lol:


Kapusta wrote:
Was Chronos named because it is fourth dimensional, a concept which is often attached with time?


Yes, it is in fact using time as the fourth dimension!

That is, under the assumption that time is zero during the manipulation
through all possible different 3D projections, we end up with an object
which consists of all those projections at the same time, i.e. a 4D object.

Of course, a finite amount of time can never be zero, the same way that
it is impossible for 3D beings like us to directly experience 4D. But by
using this assumption we achieve the closest illusion to the real thing!
(and we understand what higher dimensional symmetry is all about).

Now I need to go back to my no-windows room. Those people wearing white
are coming towards me with some huge needles.

;) :shock: :lol: :P


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