Generating Platonic Solids in C++ (2021)

FWIW a few years ago I worked on a video of 3D slices of a 4D platonic solid (a hyperdodecahedron):

https://www.oilshell.org/recurse/120-cell-bathroom.original....

It's all in Python (and shell scripts), which IMO makes it easier to experiment with than C++.

I completely forgot how it worked until I went back and looked just now ... there is this bit of 4D polytope code we borrowed, and the rest is 3D math and integration with rendering, stitching frames together, etc.

https://github.com/wwwaldo/pbrt-video/blob/master/schlafli/s...

If you’re really interested in polyhedra and how to code them, you might want to check out this resource: https://polyhedra.tessera.li/

This is missing the 6th platonic solid.

https://assets.nautil.us/8516_6a12d7ebc27cae44623468302c47ad...

I maintain a Rust crate for this and more operations like the 'dual' mentioned in the article:

https://github.com/virtualritz/polyhedron-ops

“To earth, then, let us assign the cubical form; for earth is the most immoveable of the four and the most plastic of all bodies, and that which has the most stable bases must of necessity be of such a nature. Now, of the triangles which we assumed at first, that which has two equal sides is by nature more firmly based than that which has unequal sides; and of the compound figures which are formed out of either, the plane equilateral quadrangle has necessarily a more stable basis than the equilateral triangle, both in the whole and in the parts.”

Timaeus

Doesn't include the last one to be discovered: the teapotahedron.

https://nedbatchelder.com/blog/200206/teapotahedron.html

Cool. Did similar thing years ago for a game and hve to say: it's not the mesh that gives nightmares, it's the texturing :))

Very cool, thank you!