120-cell
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- čas přidán 2. 06. 2010
- This short computer graphics animation presents the regular 120-cell: a four dimensional polytope composed of 120 dodecahedra and also known as the hyperdodecahedron or hecatonicosachoron. The figure is built up through a sequence of subsequent foldings: 5 segments form a pentagon, 12 pentagons form a dodecahedron and eventually 120 dodecahedra form the 3D shadow of a 120-cell.
The animation is included in Mathfilm 2008 DVD.
See also www.matematita.it and www.formulas.it.
The animation has been generated with POV-Ray - Věda a technologie
Excellent! It actually shows the symmetries rather than just looking like a tumor like some of the other renditions of nets of the 120-cell.
Absolutely amazing video! Makes the 120-Cell much more understandable and accessible! *Almost* I can visualize this object while watching your video. Well done!
how did you animate this without having an aneurism
probably using programming and a lot of maths
math
Wonderful! - it may be just because there's more details (lines and cells) than in the hypercube animations that I've seen, but for the first time, I could actually see how the fold into 4D works.
I got that too. I would imagine there's actually infinite ways to "assemble" the 120 cell from dodecahedra but the pair of helical chains wrapping around one another to form linked tori looks amazing and is very effective at showing a lot of structure that's normally hidden.
*My walls are now coated with brain tissue and skull fragments
looking forward to the day this becomes yet another one of those mass recommended old videos
This video really helped me wrap my head around the construction of the 120-cell. Thanks!
I'm really happy to read this! Thank you for your comment!
Gian Marco Todesco No problem. The key really was seeing how the dodecahedra are wrapped around each other in a helical fashion before being wrapped into the fourth dimension.
@@Brawler_1337 Very true. This is indeed a unique feature of the 4D space. Even the "simple" tesseract can be seen as two interlocked "chains" of cubes.
Gian Marco Todesco Yeah, I had fewer issues understanding the hyper cube since it’s so simple. It’s mainly the huge and complex polychora that give me trouble.
Beautiful Video and Music and perspectives!
How to make a 4d shape:
Make a 3d shape
*Cram smaller 3d shapes inside of the bigger 3d shape in such a way that the shape can move in the W axis*
This video is truly amazing, the author deserves many thanks, and even prizes for this.
wow! now i need the same for the 600cells
I never thought I’d be able to comprehend this shape to such a degree.
I hope the afterlife is just me watching things like this, that was beautiful
pure beauty!
Genius . I like creative people . Thank for this work
EXTRAORDINARY work!
really, really, well done. thank you.
Fascinating and sublime.
Awesome.... the shadow element was revolutionary for my ponderings... in general this video left me re-thinking my perspectives - love it when that happens! fantastically put together, presented and constructed! keep at it team! :)
The real amazing and mind bending world of topology, amazing
Wow, magnificent, Gian Marco, huge thanks!:)
I want to live in a 4D universe. : (
Take dmt
3 take it or leave it
same
Yeah, yeah ... and after a little while: "I want to live in a 5D universe."
Amazing.
Delightful!
post this clip on discord when they least expected it
wonderful, thank you so much!
my favorite shape yet
Exceptional!
Up to a point I was following along very easily...
Yes! Thank you that was awesome.
this is pretty cool
me coming here because of deltarune and seeing the people who are actually looking at the maths and making my brain explode
this is so confusing but also kinda cool
everybody wants a hecatonicosahedroid but doesnt want to admit it
Definitely!
The Magic of Math!
I hope that aliens will spare us when they see that some among us have developed the capability to understand, describe, and even visualize dimensions higher than our own
Beautiful! Although I must admit, I have a headache now.
beautiful. If only I could look at a real one.
At 0:47 you state that on the page that you are viewing the shadow, or 2-D cross section. Thank you for not ignoring this fact, shadows and cross sections is something everyone ignores in these videos. God bless you. But you for got to mention that the hyperdodecahedron was a 3D shadow, and that it was just rotating, not tensing. For example, when the shadow of the dodecahedron was on the page, what did it look like?
Two thumbs way way up!
I think I get it now...
E' meraviglioso!!
What a satanic music.
I came here cause Toby Fox put in Deltarune, in a poster:
"There some baisic shapes on this poster, a circle, a triangle, a square......................a hecatonicosachoron"
lol same. hyperdodecahedron
Ah fuvk. I wandered off too far again.
Yep, somewhat like that
what the fuck is this music holy shit
Fuckin lit brother yeeeeeeeeeeeeeeeeeeeeeewwwwwwwwwwwwwwwwwwww
Which music is this?
amazing video btw
Very shape
And that's how mass is formed. Any questions?
Dodeca-dangit. Don’t tell me you played the hecatonicosahedroid.
:)
This is a fantastic visualization tool for {5,3,3}!
Do you think you could make a comparable video of the 600-cell, {3,3,5} ("hyper-icosahedron"; its cells are tetrahedra; its vertex figures are icosahedra)?
Or even the 24-cell, {3,4,3} ("hyperdiamond"; cells are octahedra; vertex figures are cubes)?
Hi! Thankyou for your kind words. It would definitely be possible to animate also the 600-cell and the 24-cell, but it would require some effort and in this moment I'm too busy :-(
I believe that you colored it with some sort of swirlprism symmetry.
Did you compose the score yourself? It is interesting harmonically.
The composer has been a friend: Elisa Conversano
1:44 mobius strip vibes
Ooooooh. Even though it's not my field and most of the stuff I work with is generally pretty Euclidean, ooooh.
Wow this actually helped me understand this extremely complicated shape, how did you make this animation???
I was wondering the same about the animation and how it’s made…. incredible piece of work. I’ve had a ‘thing’ about the Dodecahedron for 9 years, ever since I accidentally formed one from bamboo skewers (long story) …. Here’s something I discovered about the Dodecahedron a couple of years ago czcams.com/video/mXAKv-vSvRM/video.html
The animation is nowhere near the quality of this one but I hope you find it interesting.
So Nice... Im in hipnose...
Does anyone know if you were to pause the video at 1:19 and pick out two opposite cells such that they'd be the north/south pole cells to each other, which ones would they be?
Each chain of 10 dodecahedra (6 chains per column) contains 5 pairs of opposite cells, so you just need to pick the cell that's 5 away on the same color chain on the same column
It makes sense because the dodecahedra in a chain are stacked linearly, so of course they would loop around to themselves
well that was interesting
Stunning. May I have the name of the musical piece? Fits perfectly!
1:27 is where the drugs kick in.
sick. Although I was hoping for a laptop battery hack, lol
Hi! I'm currently working on building the same polytope. How do you perform rotation from two sets of dodecahedra? looks like 4D rotation but applied on 3D objects. Thanks!
Hi. In fact it is 4D rotation applied to 4D objects. The fourth coordinate of all the vertices of the unfolded model is zero. More details by email (todesco AT toonz DOT com)
P.S. sorry for the delay
@@alparslanozafsar3435 I started with the 4D regular 120-cell. Each dodecahedron is a polychoron cell, correctly placed in the 4D space: all the vertices lie on a 4D hypersphere. I use a stereoprojection to represent the object in 3D. Initially (at the beginning of the video) the polychoron is "unfolded". There is a "root" cell; all other cells are eventually linked to this cell accoerding to a tree structure: each dodecahedron has a parent (except the root). I 4D-rotate each dodecahedron "around" the 2-face shared with the parent. When the rotation is complete the polychoron is completely "unfolded" and lies on the same 3D-space of the root that is parallel to the (stereo)projection space. Therefore the dodecahedra appear not deformed in the projection. This is what you see until 1:24. Then the cells fold again forming the 120-cell (after 1:33). Eventually the polychoron starts rotating in the 4D space (after 1:44).
@@alparslanozafsar3435thank you for your kind words! :)
You are right about the hopf fibration.
so where is the hopf fibration?
hecatonicosachoron
you broke the universe..
music?
*An axis with two directions
Very strange
The, "D" in digital became a, "B".
perhaps we are..... ?
😍😍😍😍😍✨
Maybe we are but we just can't see it. :D
raise Rigey#
Shh...there is math at work here!
...dmt.
Quite amazing and educational. The plunky music though really sucks.
But the reason you cannot see a 4-D shape or conceive or imagine one is because with every dimension there is an axis of two dimensions. 2D cross sections remove one of these axis, and so do 3D cross sections, and the consequence is the shape appearing to tense, when it is really rotating. So you are looking at a shadow. Luckily the comments weren't filled with retards, but only mind-blown civilians. Even the uploader seemed to know what he or she was doing. This gives me faith in the human race
MIND FUCK
halp
deltarune