Building 4D Polytopes

The idea behind this post goes back to a Fractal Forums discussion back in 2012, where Knighty came up with a clever scheme for ray marching polytopes. It also discusses the mathematics behind Jenn 3D (a tool for creating explicit geometry).

It is probably my most ambitious post yet – lots of interactive WebGL components – which also means it not very mobile friendly, I’m afraid.

Due to the complexity of the post, I did not use WordPress for this. Instead the blog post is hosted on GitHub, and can be found here:
https://syntopia.github.io/Polytopia/polytopes.html

Please let me know if you have ideas for improvements or corrections!

One thought on “Building 4D Polytopes

  1. Hello! This has been __extremely__ helpful in learning about polytopes and symmetry. I’m at a point that I feel comfortable with coxeter groups and with the linear algebra involved, but I’m curious about the section where you determine the normals for the mirrors; you didn’t go into much detail on finding them. I can show that the vectors you’ve provided do indeed have the needed angles, but I do not understand what algorithm you used. In particular, what would be the normal for a fourth mirror?

    Thanks.

Leave a Reply

Your email address will not be published. Required fields are marked *

*