Hypercube puzzle Abyss (4D Hyper Cube symmetry)

www.24cell.net The "Abyss" puzzle is based on the most well known 4D structure Hypercube (or Tesseract, or 8-cell). It moves between the 3D projections of the Hypercube, and it is the closest experience to 4D that a 3D object can provide to us 3D creatures.
The Abyss is solved when it has the correct shape AND the correct color pattern. The correct shape is that of a small internal cube whose corners are connected to the corners of a large external cube. The correct color pattern is achieved by having all rods of the small internal cube (and subsequently of the large external cube) to be of the same color. There are two possible solved configurations, (1) the external cube is black, and the internal cube is yellow, and (2) the external cube is yellow and the internal is black.
The goal of the puzzle is to go from one solved configuration to the other, and this is exactly what is shown in the video. During the process, we pass through an "intermediate" state with the correct shape (which is also shown), as well as many 3D projections of the 4D Hypercube.
Note: It is impossible to create a cube out of the red rods, as there are only eight of them.
This Hypercube/Abyss design was made by Pantazis Houlis by using a special type of double connectors and telescopic rods which provide a strong, flexible, and stable structure.
www.Kastellorizo.net

[@veggiet2009]

A physical model of a projected hypercube that is "rotatable" ... color me impressed, that's awesome!

[@Competitive_Antagonist]

I've always had the idea of a rotatable tesseract. It seemed like a possible, but complicated task. It's good to see someone more competent had the same idea.

[@gamemeister27]

I was not expecting it to be nearly that sturdy! Good job.

[@liliacfury]

in the fourth dimension all he would have to do is rotate it.

[@kastellorizo]

Very very true!

[@kevnar]

Actually, that's only the 3-dimensional shadow projection of a 4 dimensional hypercube. All he would be doing is rotating the shadow. The actual rotation is incomprehensible to our 3D human minds.

[@TheRMeerkerk]

@@kevnar Incomprehensible? Rotating works the same way in 4 dimensions as it does in 3 dimensions and 2 dimensions. You just have more possible rotations. The 3-dimensional shadow projection makes it look weird, because it is a shadow projection. If you look at a 2-dimensional shadow projection of a 3-dimensional cube it would look weird as well. It could also look weird if you can only see a 3-dimensional intersection and the 2-dimensional rotation plane is not embedded inside your 3-dimensional plane. If you would look at it from the right angle, then it would look the same as rotation always does.

[@ValhallaTwice]

Dude we can't see the plane on which it is rotating on. It literally would not make sense to us.

[@MelindaGreen]

Very nice! I had wanted to build exactly this model but never tried, so I'm glad that someone else did it. Like Jose, I hope that you will show us the details of the vertex construction since that sounds like the trickiest part.

[@kastellorizo]

Well... I was thinking of building a... portal to higher dimensions! :-)

[@coopergates9680]

Pretty cool to at least build something that physically can convert between projected views of a tesseract, but I admit computers are much more helpful. Do you code?

[@nicolle6620]

Bravo! After about 100 or so other videos explaining the 4th dimension aka Tesseract this one by bar far finally did it with its simplicity. Thank you

[@thefpvlife7785]

Where can this be purchased?

[@kasey42]

Ok. Where can I get one of these?

[@NICEFINENEWROBOT]

Very nice job. I had many a sleepless night pondering over this structure, imagining that I lived in one and tried to get from one room to another, finding myself suddenly walking on walls or upside down just by going straight ahead.

[@STONECOLDET944]

You have invented the 4D rabbit snare bro

[@bannistg]

Brilliant! You must make one that rotates by itself. That would be truly amazing. I think you would probably have to have it suspended in some liquid. It would be the very first 4D art in a 3D world. :)

[@AFRoSHEENT3ARCMICHAEL69]

The most complicated demo of what it be like to see a 3D cube all at once. And from our 2D perspective cause we see like pictures.

[@cpereyrav]

Esto es realmente sorprendente, lo recomendaré, saludos desde Perú!

[@gui11loup10]

Just great. Some small ajustements should be made, but that's realy a great job! Congratulations!

[@TheDavemaster300]

"Holy cow he did, the crazy son of a bi*ch did it!" LOL

[@3DICONPT]

woooooW... that´s really awesome... congrat´s... great job

[@kastellorizo]

Thank you! It took many years of effort, and the construction of many prototypes from different materials.

[@peterstiles1]

Fan-f*****g-tastic! Sir, you are awesome. Kudos.

[@CyrusBeaman]

It's been 7 years man, and you are still working on this?? I have never had that kind of patience or dedication, oh and I wouldnt consider it a puzzle if you knew how 4 dimensions work, and if you knew that was based off of a 4 dimensional cubes shadow, then it would be simple, however might I say one thing? I think you should color the cube in a way that would show that there are 8 cubes in the hypercube, just a thought

[@kastellorizo]

Well, I can be very very patient. But in the end I shall succeed! :-) The scheme was based (at that on time) on the German flag as it took part in a puzzle design competition in Germany. If you see the other puzzle (Colossus or Prometheus) based on the 24-cell, they are clearly divided into eight octahedrons. Moreover, using multiple colors for one edge can be very challenging, but it is possible to do with the normalised (i.e. right angle property) nature of the cubes. In fact, because of the (unknown to most) triality property of the 24-cell, there are three natural color schemes. I am expecting some financial support all those years, and I may be near in getting it (I hope!).

[@VTS_RUbik]

Very cool. It's only a skeleton of 3D projections of tesseract, even not 3D projection (there is no 3D volume and 2D planes, only 1D lines).

[@kastellorizo]

Even though it is a skeleton, it is a definitely 3d projection as it has height, length, and width. The nice part is that all those parameters change with the change of length of the telescopic rods. The spaces between are empty, otherwise movement which mimics the 4D symmetry would be impossible.

[@budianja4040]

awesome!!

[@MizMelysaLadi]

Very cool.

[@Himanshu12468]

okay...if we move or rotate the cube in 3D, the dimension of sides doesnt change, they neither contracts nor expands.. Can you please explain the expansion and contraction of sides in 4D?

[@kastellorizo]

Sadly, being 3D creatures, it is impossible to demonstrate faithfully a 4D movement in 3D (where all sides must always remain equal). Which is why I am using the symmetry of 4D to provide a tiny glimpse of what it looks like.

[@sumitiglesias2867]

Good job

[@arunsaravanan00]

Are they telescopic rods or hydraulic ones?

[@Armadder]

EPIC! ;u;

[@maryalcini5000]

This enlightened me to understand how it is made up of individual cubes

[@chenyangli1154]

Mary Alcini This is a tessaract projected into 3 dimensional space. Imagine projecting a cube onto a 2 dimensional surface. If you look at the projection head on you will see a small square inside a large square joined by 4 very distorted “squares”. The larger square is the surface of the cube closest to you and the smaller square is the surface of the cube furthest away from you. As you rotate the cube the 2D projection would also change. When you rotate the cube by 180 degrees the surface that was closest to you is now furthest away from you and vice versa, so the smallest and largest squares on the projection switch places. The 3 dimensional projection of a tessaract is similar, just one dimension higher up. Hence you see what seems to be a small cube inside a large cube and as the tessaract rotates, the small and large cubes switch places.

[@2shotta3]

A 4th dimensional baby playing with that, is like a baby playing with a wooden block with letters and numbers on it..

[@user-fq5jw6mj9u]

How to make this????????

[@user-fq5jw6mj9u]

I am a middle school student in Korea. We are studying dimensions. How do you make this Tesseract?

[@freedblowfish3705]

cool, but it looked better with black outside and yellow inside, should fix that

[@anjopag31]

lubiricate it

[@GregCvids]

I would definitely buy one of these! Ahem.. Kickstarter?

[@kastellorizo]

If all go well, there won't be a need for a kickstarter. :-)

[@paulthompson9668]

kastellorizo Can I buy one now?

[@DragonSageKaimus]

You should sell this models

[@joseignaciodiazgonzalez6769]

VERTEX!! how are they made

[@hl5217]

We have sucessfully came to the 4th dimension

[@klausbdl]

I WANT IT

[@35USCode]

Ok, but can you turn a sphere inside-out?

[@kastellorizo]

Long answer: By constantly manipulating the Abyss, I have seen worlds that no one has, and through inter-dimensional spacing and singular continuums, a plethora of imperative functions have been unlocked through my mind and body, enabling the ability to gather new information and achieve feats beyond my former restricted mind. Inverting a sphere of infinite symmetry is just a sporadic paradigm of many others, but can only be conceived by first trialing the aforementioned polychora. Short answer: Yes.

[@35USCode]

Whatever, Lovecraft.

[@aemiliap]

Kastelorizo congratulations! I'm convinced that exercising on visualizing other dimensions we get to change neuronal pathways. The same applies to Art I think...It changes not only mindsets but also hard wiring.Ιunderstand Art as a technology of thought and a strategy for evolution. Could you expand on how you experienced change on a somatic level?Since you are obviously Greek let me just say συγχαρητήρια!!

[@kastellorizo]

Ευχαριστώ πολύ! Και σωστά, το ιδιο ισχύει και για την τέχνη. Όσον αφορά την ερώτηση, το να ασχολείται κάποιος με νέα αντικείμενα, ειδικά όταν αυτά σχετίζονται με ανώτερες διαστάσεις (π.χ. τη συμμετρία τους), αυξάνει κατακόρυφα τη δημιουργικότητα. Ο λόγος; Νέες εμπειρίες που δεν τις έχουν ζήσει άλλοι άνθρωποι συνδυάζονται με παρελθοντικές εμπειρίες, φτιάχνοντας ένα μείγμα φρέσκιας σκέψης. Α ναι, και το όνομα γράφεται ως Καστελλόριζο με δύο λάμδα (και δύο «l» στα αγγλικά, δηλ. Kastellorizo). :-)

[@aemiliap]

σωατά -από το Καστέλλο/castello. Would that mean that you are being fortified η στ'αλήθεια ζεις στο Καστελλόριζο?

[@nurgaziutepov777]

Наверное в 4Д мире мы будем как этот автор

[@LazarevDenisBalakovo]

Про что он хоть говорил?)

[@ilyatoporgilka]

По акценту видно,что грек.

[@NoN-refundable7]

Hi man

[@nirvanadoors94]

wraio

[@dreadnots]

Very cool but not much of a puzzle..

[@kastellorizo]

Well, then how do you call doing some well thought movements? Because I've given it to many people to solve, and only a handful were up to the task. Thus, a puzzle. :-)

[@cbdrummer19]

first :)

[@ironmight4334]

Ah hah, so you started that trend!!!

[@niydfass1060]

That's just a cube inside a cube. YOU LIED TO ME.

[@kastellorizo]

It would be "just" a cube inside a cube if it was static. But this one moves, providing all sorts of 3D projections of a 4D object. Unless you live in an actual 4D world, you can't get closer than that. ;-)

[@hodorfashodor2947]

It's a cube inside a cube connected by six other cubes.

[@-_Nuke_-]

"That's just a cube inside a cube" yes, the shadow of a 4D cube is a cube inside a cube!

[@chenyangli1154]

This is a tessaract projected into 3 dimensional space. Imagine projecting a cube onto a 2 dimensional surface. If you look at the projection head on you will see a small square inside a large square joined by 4 very distorted “squares”. The larger square is the surface of the cube closest to you and the smaller square is the surface of the cube furthest away from you. As you rotate the cube the 2D projection would also change. When you rotate the cube by 180 degrees the surface that was closest to you is now furthest away from you and vice versa, so the smallest and largest squares on the projection switch places. The 3 dimensional projection of a tessaract is similar, just one dimension higher up. Hence you see what seems to be a small cube inside a large cube and as the tessaract rotates, the small and large cubes switch places.