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I maintain a Rust crate for this and more operations like the 'dual' mentioned in the article:
https://github.com/virtualritz/polyhedron-ops
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...