Again interesting, and first-rate coins!
What do you mean by "an ellipse setting for each die"?
Unfortunately F. Diederik's new message regarding his A. Pius aegis sestertius refuses to load for me.
It's the idea that you can't fit a square peg in a round hole.
If the
obverse die was set in an oval recess on the anvil and the
reverse die was set on the
face of an elliptical cylinder (see below from Wikepedia), there would be only two orientations of the dies possible when they were fitted together for striking provided the dies themselves were oriented along the long
axis or short
axis an ellipse (see a and b below). If one die was oriented on the long
axis and the other on the short
axis, they will be at right angles when struck.
I can't open the A. Pius
aegis thread either for some reason