Sorry, I meant miPmap, the autocorrect replaced it
Mipmaps are scaled down versions of a texture that are used to avoid aliasing or artefact when a texture, mapped on a mesh, is seen from far away.
Yeah, that makes sense. Well it seemed like mipmap was enabled on my mesh, and I turned it off according to these instructions, but it had no effect.
What happens of you instead use an Ico-Sphere, and adapt your texture to the unwrapped form of that?
My thinking is that, if this is some sort of (possibly-mip-mapping-related) issue caused by the narrow triangles at the poles, and their likely-stretched UVs, then perhaps one solution is to use a type of sphere lacks that feature.
I’m almost sure that would fix the problem, since there would be no near-discontinuity at that point. Do you know how I can convert my texture image to an ico-sphere format?
(As a further safeguard, I might suggest using the “Smart UV Project” UV-mapping tool, if your version of Blender has it. The resulting map–as generated on my machine, at least–is more awkward to work with, but doesn’t seem to have any stretched triangles.)
For me, it seems to have the same stretched triangles at the poles.