Incidentally, your quartic surfaces page seems rather unclearly written in places. It took me a while to twig that the quartic surface equation given in the page title was not in fact a typo but was talking about rational rather than integer solutions. Then you shift from that representation straight to adding a t⁴ term and talking about integers, and suddenly shift back again in the hyperplanes section.

With a bit of thought it's not impossible to work out what you're talking about, but I think I'd prefer that you only require thought of your readers in the bits that are actually supposed to require thought :-)