More on the rotated sphere, especially the ellipse that is the equator.

1. Rotated sphere: a of the equator.
Sharon Liu.
2023/08/31.
Disclaimer: I think this is correct. I am not completely sure.
This is a sphere which is rotated 45 degrees down, and 45 degrees to the left.
The a of the equator, helps to define the shape of the ellipse (the equator). It is the point at the end of the short axis, of
the ellipse. a is located, at the back of the sphere.
From your top left, to bottom right:
North pole (x, y, z): (-½, 1/sqrt(2), -½).
South pole (x, y, z): (½, -1/sqrt(2), ½).
a (x, y, z): (-1/sqrt(12), 2/sqrt(24), 1/sqrt(12)).
a was found, by drawing 2D triangles, including triangles in the plane y = (-2/sqrt(2))x, plane xy, plane xz, and plane zy.