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 Post subject: Infinity (based on 5D Symmetry)
PostPosted: Thu Jun 09, 2011 8:05 pm 
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Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
Infinity is a very cute puzzle which uses the symmetry of the five dimensional
structure of the 5-simplex. It is similar to the Pegasus puzzle I did last time,
but now it is edges which are colored, and this gives a meaningful goal to this puzzle.

When minimizing all external rods, the puzzle takes the shape of a solid with a
square base and six triangular faces (Heptahedron). In any case, after making
an extensive search, I had the need to categorise the series of solids which have
a square/rhombus base and the two opposite vertices have a set of new vertices
which are placed at the top and belong to the same "arc" which creates a circle
vertical to the line formed by the other two opposite vertices of the base. Let's call
them as Pantahedron-n (where n is total number of vertices). For example,
in this case we have six vertices, so it is a Pantahedron-6. Pantahedron-4 is the well
known Tetrahedron (not included in the image).

Attachment:
Pantahedrons.jpg
Pantahedrons.jpg [ 22.66 KiB | Viewed 949 times ]


This type of shape is very common when it comes to Higher Dimensional symmetry (HDs)
structures using telescopic rods and are based on the Complete Graphs Kn, but no specific
name had been given to this category (instead each of those shapes belong individually to
other differently named series).

The goal is to create in the middle the infinity symbol using a specific color.

Attachment:
Infinity_yellow_01.jpg
Infinity_yellow_01.jpg [ 161.81 KiB | Viewed 949 times ]


Solved position with the yellow infinity symbol.


Attachment:
Infinity_red_01.jpg
Infinity_red_01.jpg [ 165.79 KiB | Viewed 949 times ]


Solved position with the red infinity symbol.

As a puzzle, Infinity is quite challenging, as unlike Chronos, it requires more than one types
of moves (some are combined, like in the Houlis Cube) to go through its 36 states (72 if we
don't count the trivial ones). And going from one state to another requires a few elongating
and contracting Inside-Out-Turning (IOT) moves.

:)


Pantazis

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 Post subject: Re: Infinity (based on 5D Symmetry)
PostPosted: Fri Jun 10, 2011 11:25 am 
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Joined: Thu Sep 24, 2009 12:21 pm
Location: Chichester, England
Very snazzy. I love these puzzles. In fact, I believe it was you who has encouraged me to not just limit myself to twisty puzzles (even though the only puzzles I have which aren't twisty are a Magic and Laurie's puzzle). Very nice. :)

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 Post subject: Re: Infinity (based on 5D Symmetry)
PostPosted: Fri Jun 10, 2011 12:31 pm 
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Joined: Wed Jan 28, 2009 7:55 pm
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Not only do you have a monopoly on this genre of puzzles but on the forum as well. All recent posts on the forum are from your thread all the way back to Mutually Constrained Cubes.

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 Post subject: Re: Infinity (based on 5D Symmetry)
PostPosted: Fri Jun 10, 2011 1:40 pm 
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Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
Luke wrote:
Very snazzy. I love these puzzles. In fact, I believe it was you who has encouraged me to not just limit myself to twisty puzzles (even though the only puzzles I have which aren't twisty are a Magic and Laurie's puzzle). Very nice. :)


Thanks Luke, and I am sure you will also come up with some great idea,
as long as you keep searching for new stuff! :)


Rentlix wrote:
Not only do you have a monopoly on this genre of puzzles but on the forum as well. All recent posts on the forum are from your thread all the way back to Mutually Constrained Cubes.


I could list them separately, but it is the usual PAJUPUMA! (Pantazis June Puzzle Madness!)
And I am not done yet... :wink:

:lol: :P


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