I believe it's the fact that the resolution of the mesh is so low that the angles from face to face are so sharp that the SSS sees it as a corner that is thinner and thus lightens it up (expected from SSS, but rather extreme). The sharper the corner the brighter. As soon as i added a lvl 1 subsurface modifier, it made the surface smooth enough geometry wise to calculate the surface as if it was one rounded shape.

The fact that if you change the shading to **Flat Shading** the brighter lines along the sharp folds of the faces becomes even more pronounced makes me sure that SSS really only gives that result because on the low resolution surface.

Here a comparison with a quadsphere with just one point dragged out to create an extreme that the SSS instantly shades as it did in the file shared.
[![enter image description here][1]][1]<br>
Also visible here is that the quads seem to be internally triangulated and the resulting edges are generating the thinner corners or folds which get calculated by the SSS algorithm. Specifically the "Volumetric" version used in **Random Walk** as that is a volumetric approximation of a physically based volume scattering.

While it was not asked for a solution, i would still think that a level 1 subdivision modifier should get rid of the pattern.

  [1]: https://i.sstatic.net/bWmEJ.png