These videos are of 4D objects (regular polytopes) translating through a direction that is perpendicular to our familiar 3.

If you have suggestions for creating videos that involve taking 3D cross-sections of 4D objects please let me know!

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestIt's amazing how complicated things can get just by generalizing the 3D icosahedron into the 4D version of it. Wow. The number of parts just explodes: 600 cells, 1200 faces, 720 edges, 120 vertices. Compare that with only 20 faces, 30 edges, 12 vertices of an icosahedron. We are only seeing glimpses of this complexity with this video. – Michael Mendrin · 1 year, 4 months ago

Log in to reply

– Roberto Nicolaides · 1 year, 4 months ago

Yeah. I wish that there were more generalisations of this in higher dimensions though! If you have any suggestions for making more videos on this object let me know.Log in to reply

In checking the current CG software market, it's interesting to see that AutoDesk has bought out Alias, and now they have "Maya 7", a pretty sophisticated package that can deliver movie quality animation. In the bad old days, you bought the package anywhere from $20K to $100K, but you can subscribe to Maya 7 for about $123 a month. Still out of range for most people that are not professionals. However, AutoDesk may have something free for students. Check this out AutoDesk – Michael Mendrin · 1 year, 4 months ago

Log in to reply

– Roberto Nicolaides · 1 year, 4 months ago

Apologies, I did not make myself clear! I'm one of the creators of this video (using Python 2). I should've said "Are there any more videos of 3D cross-sections of 4D shapes that anyone would like to see?"Log in to reply

Hypercube Cross Sections. It seems like most people aren't getting it. I think a note or wiki explaining this would be great. – Michael Mendrin · 1 year, 4 months ago

Wow, you did not make yourself clear! That is quite an accomplishment, to have done this with Python. I know it would have taken me a while using Mathematica. I think this sort of thing could make an excellent series of notes or even wikis. I can think of something right now that you could help with. Have a look at Zandra Vinegar'sLog in to reply

This is really beautiful work. – Michael Mendrin · 1 year, 3 months ago

Log in to reply

– Roberto Nicolaides · 1 year, 3 months ago

Thanks Micheal, it's part of a project at Uni. Most of the credit should go to my supervisor though! By the way, whenever I take a 3D -cross-section of the 600-Cell it always seems to have square and/or triangular faces. Is this always true and is there an intuitive reason why?Log in to reply

– Roberto Nicolaides · 1 year, 3 months ago

Just realised the answer! It's because it's made of tetrahedral volumes and a 2d cross-section of a tetrahedron is always a square or triangle (generically)!Log in to reply

Using the same thinking, we can figure out the correct answer to Zandra's hypercube cross-section problem. – Michael Mendrin · 1 year, 3 months ago

Log in to reply