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 Post subject: Houlis Cube, an intro to the 4-dimensional puzzles (+videos)
PostPosted: Mon Jul 05, 2010 6:18 pm 
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UPDATE: Have added two videos (also linked below)
http://www.youtube.com/watch?v=Ft8aOtf6dx0
http://www.youtube.com/watch?v=k2YSy9_iOmw


This is the first post I reveal regarding a new type of puzzles, which are based on four-dimensional
symmetry. They are amazing objects (not just puzzles) and I have been so intrigued by them,
that the past months I have hardly played with any other puzzles.

I present the Houlis Cube, which is called like that because of the X's that exist on each side of the cube.
In Greek, my name is "Χούλης" (i.e. it starts with "Χ" which is pronounced as "H" in English).

Attachment:
4D_Houlis_Cube.jpg
4D_Houlis_Cube.jpg [ 100.39 KiB | Viewed 7616 times ]

(the photo was taken at the island of Kastellorizo, around a week ago)

The patent for all such structures has been filed some time ago, and the way it works is very efficient
that is, the edges do not get tangled (I guess this is where many had failed in the past, that is, *if* there
were any efforts).

In the picture, the puzzle is solved (it has two solutions). But the X's can be scrambled in many ways,
and this puzzle includes some serious challenges. Unless, you are living in the fourth dimension.
Then, it will be too easy for you to solve!

I will not speculate more, I will love to first see people scratch their minds a bit. Videos will follow, while
those meeting me in the next days, are in for some real treat! Good morning from Singapore!

;)


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Last edited by kastellorizo on Wed Jul 07, 2010 3:07 am, edited 2 times in total.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 6:21 pm 
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May I be the first to say.... wow! I am thoroughly confused, but in a good way...

-pi (Eitan)

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 6:33 pm 
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You certainly have caught my attention. You seem to have a knack for making puzzles that are completely unique and have no relation to anything else ever made. I am anxious to see more of this puzzle.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 6:41 pm 
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Anyone notice that these things always come out, just as we're starting to get comfortable (ie with the jumbling topic)? :lol:

I'm still not quite sure what I'm looking at, but I can't wait to find out!

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 6:51 pm 
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I think I may be able to try to begin to understand what the movement might be kind of like someday.

At the moment I do not.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 6:54 pm 
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Looks nice! Not sure what it does exactly, the photo doesn't really show that too well, but any physical implementation of a 4D puzzle is seriously impressive and cool! I REALLY want to find out more about your 4D puzzle ideas (I love 4D puzzles ... and higher than 4D ones too ...).

Keep the updates coming Pantazis!

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 6:55 pm 
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kastellorizo wrote:
I will love to first see people scratch their minds a bit.


Consider my mind scratched. I love thinking about 4D stuff but its always a struggle.

And you probably should say 4 spatial dimentions, otherwise we all live in 4D spacetime.

Hmmm... acording to string theory there are what 10 spatial dimentions? After hight, width, depth, has ANYONE ever seen a name for the others? I understand we can't see them but surely we should be able to name them. Sorry for the extra-dimensional tangent off in the Zaphod direction.

Carl

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 6:59 pm 
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Wow, that's a good tease, can't wait to see some videos. It reminds me of a 'Brainstring', idk, with its tangled strings. Am I way off?

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 7:03 pm 
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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 7:08 pm 
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To answer some questions:

1. Yes, after the odd-numbered and triangular folding puzzles, gravity puzzles (air or water)
I tend to always "chase" not just new puzzles, but new classes of puzzles. And more to come in the future. :)

2. It surely looks impressive (terminator-like). But moving it, is 1000 times more impressive!!! ;)

3. I am using time as the fourth dimension, and I will soon explain why and how.

4. Yes, I have already made puzzles which use higher than 4-dimensions symmetry (e.g. 5th and 6th dimension).

5. It has absolutely nothing to do with the Brain String, and it moves very smoothly.


Hint of how it is supposed to be solved: Turn it inside-out! (which requires a lot of key sequential moves)

8-)


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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 7:20 pm 
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kastellorizo wrote:
Hint of how it is supposed to be solved: Turn it inside-out! (which requires a lot of key sequential moves)



I think I got it on how it moves. The segments collapse and expand like a pump or a suspension, right?

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 7:23 pm 
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gabrielmpf wrote:
kastellorizo wrote:
Hint of how it is supposed to be solved: Turn it inside-out! (which requires a lot of key sequential moves)



I think I got it on how it moves. The segments collapse and expand like a pump or a suspension, right?

I think that's a solid guess.

I've been waiting for news since I saw the chronos on the IPP page.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 7:24 pm 
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gabrielmpf wrote:
kastellorizo wrote:
Hint of how it is supposed to be solved: Turn it inside-out! (which requires a lot of key sequential moves)



I think I got it on how it moves. The segments collapse and expand like a pump or a suspension, right?


Exactly. In four dimensions, the notion of "length" is a lot different to the one perceived in the 3D world.

:mrgreen:


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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 7:32 pm 
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Nice idea. I hope you didn't snap off too many car radio aerials/antennae to make this thing. :lol:

For those who are still wondering about movement, here are a couple of animations of 4D cubes and pyramids from wikipedia (you might recognize the hyperpyramid from this year's IPP puzzle competition :wink:):

Image

Image

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Last edited by KelvinS on Mon Jul 05, 2010 7:35 pm, edited 2 times in total.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 7:33 pm 
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Pantazis, how big is it? I can't get any sense of scale with that picture.


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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 8:46 pm 
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Jared wrote:
Pantazis, how big is it? I can't get any sense of scale with that picture.

im guessing about golden cube size.

this looks cool but i dont quite understand it


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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 8:57 pm 
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I really can't wait for the videos of this.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 9:23 pm 
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kastellorizo wrote:

Exactly. In four dimensions, the notion of "length" is a lot different to the one perceived in the 3D world.

:mrgreen:


Pantazis



must it be solved in a certain amount of time? the 4th dimension is time if I recall correctly, and a length there would be a time period.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 9:35 pm 
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oh! oooohhhh!!!!
Okay, that makes sense... so it's not ACTUALLY 4 dimensional, just the 3d shadow of the 4d world... even so, it's astounding!
I've always wondered if something could be made to move in the way that 4d objects do.

(it's probably still not quite what I think though.... we'll see...

edit: there's a hypertetrahedron too??!!! :o :shock: :o :| :P

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Mon Jul 05, 2010 11:45 pm 
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The 4th spatial dimension isn't time.

If you've never read flatland, I suggest reading it before attempting this puzzle. I'm sure it'd help?

Basically, a 4th dimensional being would be able to see not only your outside, but your inside at the same time. Like how you can see a WHOLE SQUARE, not just a line.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Tue Jul 06, 2010 12:23 am 
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I love 4d!!! Even if this has nothing to do with hypercubes, I can't wait for this puzzle :mrgreen:

This looks so cool :!:

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Tue Jul 06, 2010 4:48 am 
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ulmboy556 wrote:
kastellorizo wrote:

Exactly. In four dimensions, the notion of "length" is a lot different to the one perceived in the 3D world.

:mrgreen:


Pantazis



must it be solved in a certain amount of time? the 4th dimension is time if I recall correctly, and a length there would be a time period.


Yes, a certain amount of time for 3D beings. But for 4D beings, both solutions
(and in fact, *all* states, scrambled or not) exist at the same time!

By solving it, you are forced to go through all 3D projections of a 4D object,
which in this case, is the 16-cell. Therefore, by assuming that time is/tends-to zero
during the solve, we manage to see all states/shapes/projections at the same time
and so we can deduce that we hold the closest thing to a 4D object which can be perceived
in the (limited) 3D world.

Now, you may want to learn about all possible 3D projections of this 4D object,
but trust me, you *do not* want to know the 4D expansions of *ourselves*!!!

:lol:


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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Tue Jul 06, 2010 5:14 am 
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LOLWUT?? :lol:

:D Greg :D

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Tue Jul 06, 2010 6:58 am 
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Here it is: a 3D projection (shadow) of the 4-dimensional 16-cell, from the article in wikipedia:

Image

The starting "X-cube" configuration shown in the photo is one special 3D projection of this 4D shape...

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Last edited by KelvinS on Tue Jul 06, 2010 7:12 am, edited 6 times in total.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Tue Jul 06, 2010 6:59 am 
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After a decent amount of time staring at this picture, I am pretty confident I understand the movement of this puzzle. I can't wait for a video though!

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles
PostPosted: Tue Jul 06, 2010 7:48 am 
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Video here:

http://www.youtube.com/watch?v=Ft8aOtf6dx0


Enjoy, and be careful to check your brain muscles after watching it,
just in case they take the form of the Moebius strip!

:P


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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 8:24 am 
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MIND = BLOWN.

When are these up for sale?

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 8:36 am 
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theVDude wrote:
MIND = BLOWN.

When are these up for sale?


Remember, the word "when" does not make sense in the 4th dimension!

:lol: :P


Pantazis


PS. On a serious note, I have no idea when we will start selling them!!!
But it will happen sooner or later.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 9:54 am 
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kastellorizo wrote:
theVDude wrote:
MIND = BLOWN.

When are these up for sale?


Remember, the word "when" does not make sense in the 4th dimension!

:lol: :P


Ofcourse it does, the word where makes perfect sence in the 3d world, "when" just becomes another coordinate.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 10:27 am 
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Namegoeswhere wrote:
kastellorizo wrote:
theVDude wrote:
MIND = BLOWN.

When are these up for sale?


Remember, the word "when" does not make sense in the 4th dimension!

:lol: :P


Ofcourse it does, the word where makes perfect sence in the 3d world, "when" just becomes another coordinate.


As already stated in (more than one) of my previous replies, not in the same way we perceive it in 3D.
(this conclusion can be easily made to clarify what I meant, that is, if my sequence of thoughts is followed)

;)


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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 12:03 pm 
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So obviously there will be a 600-cell-shaped one sooner or later, right? :twisted:


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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 12:41 pm 
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Not sure why you keep taking about time being the fourth dimention here (some sort of joke I hope!), my understanding of it is that it is the the 3D projection of a shape in 4 geometric dimentions. Instead of having the usual 3 axes which are mutually perpendicular (x,y and z), if you model what would happen if there were 4 dimentions of space at right angles to each other (x, y, z and w) then this is one of the shapes you can get, the 16-cell. It is the 4D version of the octahedron (both part of the cross-polytope family), so it's simplest coordinates would be all the permutations of (+/-1,0,0,0). It is also the dual to the tesseract (4D cube for those who don't know), which is why it can be projected as a cube. Lastly, it has the symbol {3,3,4}. Wikipedia has more info :)

An amazing idea Pantazis, and I can't wait to get my hands on one and see the rest of the collection. You are a genius! :D

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 12:57 pm 
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bobthegiraffemonkey wrote:
Not sure why you keep taking about time being the fourth dimention here (some sort of joke I hope!), my understanding of it is that it is the the 3D projection of a shape in 4 geometric dimentions.



I will try to explain it briefly:

A 4D creature can view all 3D projections at once. We, 3D creatures, need a little bit of time...!
Which is why I said that *if* we assumed that the time it took us to view all 3D projections
(enabled by the structure) was zero, then we would feel like a 4D creature does!

But of course, this "viewing time" can never be zero in 3D, but at least we are allowed to assume,
and have some "similar illusion" that we can emulate this unique feeling, this time in the physical
world, without using visual or virtual effects.

It is a delicate point, where time can be considered spatial in a... reversible way!
I hope I can make sense, otherwise, you may see me soon at the madhouse! LOL

:)


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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 12:59 pm 
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Jared wrote:
So obviously there will be a 600-cell-shaped one sooner or later, right? :twisted:


Trust me, there is some smaller *and* bigger structures waiting to be revealed...
the biggest one so far is Colossus. I will not reveal it now, please be patient!

:)


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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 1:06 pm 
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Time is a fourth dimension, but not a spatial dimension.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 1:12 pm 
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theVDude wrote:
Time is a fourth dimension, but not a spatial dimension.


There is a big debate between scientists of how time is related to this. The "snake" for example.
(for us 3D creatures, time is not reversible, for others, in 4D, it may well be reversible!)

It all boils down to the definitions. It has even been a talking point at the forum some
time ago, but I only use some of this mystery term to "dress" the new 4D class of puzzles.

:)


Pantazis


PS. I need to reveal here that the Puzzle Ninja lives in the 5th dimension! :P

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
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kastellorizo wrote:
PS. I need to reveal here that the Puzzle Ninja lives in the 5th dimension! :P

Which is henceforth known as the Trihx dimension!

I need to read more on higher dimensions. And get back into the math for them, too.

It's been too long.

EDIT: I figure I should add to this what I think of the fourth spatial dimension by bringing it down and comparing 1 dimension to 2 dimensions, and 2D to 3D. New thread in off topic here

1 dimension would be a line. This is Lineland, and the inhabitants are lines of varying length. They are free to move about in one dimension (for this example, EAST and WEST) until they come upon their neighbor, where they are forced to stop. An example of a typical lineland dweller and his neighbors would be like this:
Code:
.______.      .___.        ._____.

The dots on the picture show each end of the linepeople in this example, and the line would be their insides.

In the 2D world(flatland), you have 2D beings (lines, triangles, squares, pentagons, ... , circles). They're free to move about in their two dimensions, so north, south, east, and west. They have no concept of up or down, because they live on a 2 dimensional plane. An example of a Flatlander would be like this:
Code:
┌──┐
│  │
└──┘


Flatlanders, however, cannot tell each other apart by sight because all they see when they see each other is a one dimensional line. You can do the same thing by taking a coin and holding it sideways. The circular coin becomes a line.

As 3D beings living in space land, we have 3 dimensions through which we can move (north, south, east, west, up, and down). We can also see the insides of the lower dimensional beings (you can see not only the square above, but inside it), and could even interact with their insides WITHOUT touching their outsides (the lines that make the square). Just as the 2D square could do to the people in lineland, IF lineland was along flatland's plane.

Questions this raises for me, without even going into the 4th dimension, are questions like:

If a Flatlander took a linelander off their line, would their insides fall out? If a spacelander took a flatlander off their plane, would their insides fall out?

In both cases, there's nothing protecting the being (flatlander or linelander) from this new dimension.

Now, into the 4th dimension. There is a 4th dimensional being, looking down at our 3D spaceland. Just as we in spaceland looked down and saw inside and outside of the people of flatland, the people of 4D would look down and see us inside and out. If they wanted to they could reach into us, poke our organs, and never touch or pass through our outside.

Just as the flatlanders can only see in 1 dimension, our vision is limited to 2 dimensions. As humans we work around this with perspective and depth perception, but we're still receiving flat images all the time. 4 dimensional beings would see in TRUE 3D, something I can't even begin to imagine. Sounds cool though.

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Last edited by theVDude on Tue Jul 06, 2010 1:49 pm, edited 2 times in total.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 1:42 pm 
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Simply amazing as always! I love the forth dimension. All you need to make now is a magic 600-cell! :lol:

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 1:59 pm 
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As if Oskar's repeated universe breaking was not enough, now Pantazis is getting in on the act. If there is any truth to the Doomsday 2012 predictions, I have a sinking feeling that these two manipulators of space and time will build something that not only breaks the laws of physics but completely shatters the space-time continuum.

Anyways, I await the arrival of the Houlis Cube's brethren, even if they bring us significantly closer to the end of the world as we know it.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 2:29 pm 
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I'm not that impressed by this. I don't really see this as an accurate representation of a 4D puzzle. I think too many of you just hear 4D and start drooling before you really understand what it is.

It's still a cool puzzle. I just don't think this qualifies as a 4D puzzle.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 3:03 pm 
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I need to see the 8 cell, although that wouldn't be much of a puzzle since turning it inside out would be extremely easy...
And even more needed is the 11-cell!!

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 4:01 pm 
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GuiltyBystander wrote:
I'm not that impressed by this. I don't really see this as an accurate representation of a 4D puzzle. I think too many of you just hear 4D and start drooling before you really understand what it is.

It's still a cool puzzle. I just don't think this qualifies as a 4D puzzle.


This puzzle has *clearly* 4D symmetry, it uses it in its every single move, and by moving
*and* contracting edges, it directly applies the 4D theory. I am not sure why you say this...

Please let me know if you personally know *anything else* that even remotely comes close to my puzzle(s).
I mean, you are entitled to your opinion, but I have never seen before such structures,
which is why I spent heaps of time and thousands of dollars to create some prototypes.
I repeat, look at the symmetry it uses: it is 4D *by definition*!

Yes, in the past we have heard many "4D puzzles" NONE of which used the proper 4D symmetry.
And here they are, for the very first time. You will realise this, when more designs are unfold. ;)
(I do not expect people to directly embrace designs which are based on work of years).

Also, this is no virtual implementation, it is a *real* existing proof of concept.

If you have no alternatives to this to propose, what would *you* call as a 4D puzzle?
(which *has* to use 3D projections).

Finally, you do not seem to grasp the importance of bringing to life such structures, which in
this forum, were deemed impossible to create, many many times. The new doors it opens
can only be mind boggling, and I personally hope to see more unique puzzles by others here,
as I regard the people in this forum of excellent intelligence.

Regarding some other questions, there exists the 8-cell plus many more. I will reveal them
in the next days. The best one is Colossus, a beast of a puzzle!!!

:)


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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 4:12 pm 
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The Colossus sounds cool.
I agree with GuiltyBystander kind of. This puzzle is great looking and really really cool but it is not a 3x3x3x3 which would be a true 4d twisty puzzle (and be impossible :lol: )
I agree that it's 4d but not the same as the 4d or 5d puzzle programs that exist.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 4:16 pm 
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PuzzleMaster6262 wrote:
I agree that it's 4d but not the same as the 4d or 5d puzzle programs that exist.
Which he never claimed. He said it's a puzzle that uses 4D symmetries (in the hints thread a while ago, even). I didn't quite follow the video (it was being choppy, I was on my netbook) but I'm more interested in the chronos, the hypertetrahedron.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 4:19 pm 
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It would be great to see a frame-by-frame animation of this puzzle following the exact same shapes and transformations as seen in the animation from wikipedia, attached above. That would surely demonstrate how closely this resembles the 16-cell symmetry.

Meanwhile, I've just succeeded to create a zero-dimensional puzzle - it's at the end of this sentence.

:P

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 4:19 pm 
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PuzzleMaster6262 wrote:
The Colossus sounds cool.
I agree with GuiltyBystander kind of. This puzzle is great looking and really really cool but it is not a 3x3x3x3 which would be a true 4d twisty puzzle (and be impossible :lol: )
I agree that it's 4d but not the same as the 4d or 5d puzzle programs that exist.


I see your point and I think I know where the mind block is:

- The 3x3x3x3 is first a puzzle which becomes 4D

- The Houlis Cube is first 4D which I made into a puzzle

I hope things are more clear now! :)

Edge transitivity, regular polychoron (i.e. polytope) properties, are things directly found
on the new puzzle I presented, but it is not found on the 3x3x3x3.

In other words: I am starting directly from the 4D source.

:)


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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 4:21 pm 
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Kelvin Stott wrote:
It would be great to see a frame-by-frame animation of this puzzle following the exact same shapes and transformations as seen in the animation from wikipedia, attached above. That would surely demonstrate how closely this resembles the 16-cell symmetry.
I agree, a stop-motion of the movement (if possible) would be nice. Physically moving the puzzle with your hands stopped me from clearly seeing... the movement of the puzzle, really.

Kelvin Stott wrote:
Meanwhile, I've just succeeded to create a zero-dimensional puzzle - it's at the end of this sentence.

:P
Don't try to hijack this thread with that amazing puzzle, it deserves a thread of it's own!

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 4:24 pm 
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I wonder what would happen if Kasterllorizo and Oskar did a collaboration? A Mix-Up 3x3x3 that can turn inside out at will?

Honestly, about the 4-D discussion, it all boils down to whether you are talking about spacial dimensions.

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Last edited by Ender Delphiki on Tue Jul 06, 2010 4:39 pm, edited 1 time in total.

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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 4:24 pm 
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Kelvin Stott wrote:
It would be great to see a frame-by-frame animation of this puzzle following the exact same shapes and transformations as seen in the animation from wikipedia, attached above. That would surely demonstrate how closely this resembles the 16-cell symmetry.


Indeed. I have made one for Chronos, which people at the IPP will be able to see.
All 3D projections are clearly shown (In fact, I have the patent images, but I cannot
show them yet).

It is used on the solution sheet to demonstrate the correct move, which not only makes
the life easier for those solving it, but it also prevents people from abusing the puzzle! LOL

Kelvin Stott wrote:
Meanwhile, I've just succeeded to create a zero-dimensional puzzle - it's at the end of this sentence. :P


LOL I did not see *that* coming!!! *confused now*

:)


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 Post subject: Re: Houlis Cube, an intro to the 4-dimensional puzzles (+video)
PostPosted: Tue Jul 06, 2010 5:42 pm 
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I think I understand now Pantazis, I maybe jumped to conclusions earlier (my last post was a little rushed lol). Here is my new interpretation, please feel free to correct me if I'm still wrong. The 16-cell is a 4D shape, in that it exists in 4 spatial dimensions, where the fourth dimension is not time, but a dimension of space at right angles to the 3 we are familiar with.
However, we people living in 3 spatial dimensions cannot see in four spatial dimensions, only 3*. Since the 4D shape can be thought of as consisting of 3D slices (like a cube can be thought of as having 2D, square slices), viewing a sequence of these 3D slices is sort of equivalent to a 4D being seeing in four spatial dimensions and obtaining the same effect by being able to see the shape's 4D 'depth'. Therefore, it is possible to substitute the fourth dimension typical of this shape, a fourth geometric dimension, by our 'fourth dimension' of time by seeing the 3D projections in sequence. Something like that?

If so, that's a strange way of explaining this 4D implementation, but it's brilliant! :D

*I see the argument why we only see 2D, but since our eyes see slightly different 2D images it effectively makes a 3D image. Just my thoughts.

Matt

PS. In my last post I continually said 'dimention' instead of 'dimension'. My bad :oops:


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