Does every sum-of-squares equation have a plane geometric interpretation?

Question

The 2.1.2 sum-of-squares [SOS] equation $$a^2=b^2+c^2$$ can be thought of in the [regular XY] plane as a right-angled triangle.

Question: Is there an analogous interpretation for every SOS equation?

For example, does the 2.1.3 SOS equation $$a^2=b^2+c^2+d^2$$ have an interpretation in plane geometry?

Answer 1

$$ a^2=b^2+c^2+d^2 \quad\hbox{and}\quad p^2+q^2+r^2=s^2+t^2. $$