20261102 110004 barth6 s3 hemispheres

Description:
The Barth Sextic in 4-variable projective form intersected with a unit 3-sphere, projected into three variables stereographically as we move the affine chart around, and move the camera around. this is a periodic movie ;) computed with my new in-progress port of bertini_real, using bertini 2 as its backend. the black dots are the singularities. the pieces "cut off" as they intersect with the sphere, but they're really teleporting across the sphere antipodally. see also the inspiration, at https://blogs.ams.org/visualinsight/2016/07/01/barth-decic/ .

I used Claude heavily to help write the code for this. It's taken like 8 months to write this stage of the code, on top of what I manually wrote from 2013-2026. So no, this isn't AI slop. It's the culmination of 13 years of work on this topic. I regard this as experimental mathematics.