Marek! I got it! Remember that function that was supposed to morph a tiger into a ditorus, that
you wrote here?
Well..... I just experimented (and self-discovered what you did), and came up with the proper equation. This time, the two tori are perfectly formed, and maintain their shape under rotation, between the vertical stack and side by side cuts. It's also the non-bisecting general plane equation that does what you are looking for. The culprit all this time was a squaring of terms that didn't need to be.
What you had before was:
(sqrt(x^2 + ((sqrt(y^2 + b^2) - 4)^2*cos(a) + z*sin(a))^2) - 2)^2 + ((sqrt(y^2 + b^2) - 4)^2*sin(a) - z*cos(a))^2 = 1^2
What ends up working is:
(sqrt((x*sin(a) + (sqrt(z^2+b^2)-5)*cos(a))^2 + y^2)-3)^2 + (x*cos(a) - (sqrt(z^2+b^2)-5)*sin(a))^2 = 1
where the (sqrt(z^2+b^2)-5) term doesn't need to be squared, since it already is. So, how about that?
A fully 4D equation ends up as:
(sqrt((x*sin(a) + (sqrt(z^2+w^2)-5)*cos(a))^2 + y^2)-3)^2 + (x*cos(a) - (sqrt(z^2+w^2)-5)*sin(a))^2 = 1
where parameter 'a' will adjust the non-bisecting plane of rotation. What's really interesting about the result of this function, is getting the two tori in the exact positions needed to express a mantis cut. We're now 2/3's of the way there. Next step is how to add another torus, and pair it with the other two. Easier said than done.